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11.03.2020

Solve using elimination. x − 8y = 19 9x + 8y = 11 (, )

Step-by-step answer

09.07.2023, solved by verified expert

Rajat Thapa

s Specialist

Mathematics, DAV Post Graduate College

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Step-by-step explanation:

Let's add together the two equations

At this point I would recommend simply using the value of x in the firs equation to find y.

Or just multiply the first by 9 and subtract the second.

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Mathematics

Solve using elimination. x − 8y = 19 9x + 8y = 11 (, )

Step-by-step answer

P Answered by Specialist

(3;-2)

Step-by-step explanation:

Let's add together the two equations

$I + II : x-8y +9x +8y = 19+11 \rightarrow 10x=30 \rightarrow x =3$

At this point I would recommend simply using the value of x in the firs equation to find y. $3-8y=19 \rightarrow -8y=16 \rightarrow y=-2$

Or just multiply the first by 9 and subtract the second.

$9\times I-II: 9x-72y-9x-8y=171-11 \rightarrow -80y=160 y=-2$

Mathematics

5x-y=13 X+8y=19 Solve by the elimination method

Step-by-step answer

P Answered by PhD

x=3, y=2

Step-by-step explanation:

To solve by elimination method, multiply one of the equation by a constant such that when you subtract one equation from the other, you are left with one term only.

Mathematics

5x-y=13 X+8y=19 Solve by the elimination method

Step-by-step answer

P Answered by PhD

x=3, y=2

Step-by-step explanation:

To solve by elimination method, multiply one of the equation by a constant such that when you subtract one equation from the other, you are left with one term only.

Mathematics

Solve the system using either Gaussian elimination with back-substitution or Gauss-Jordan elimination. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, set y = t and solve for x in terms of t.) −3x + 5y = −19 3x + 4y = 1 4x − 8y = 28

Step-by-step answer

P Answered by Master

x = 3 and y = -2

Step-by-step explanation:

We have the following system:

-3 5 | 19

3 4 | 1

4 -8 | 28

We divide the first row by -3 and it would be:

1 -1.67 | 6.33

3 4 | 1

4 -8 | 28

Now, we multiply by 3 and subtract the second row and we have:

1 -1.67 | 6.33

0 9 | -18

4 -8 | 28

Now, we multiply by 4 and subtract the third row and we have:

1 -1.67 | 6.33

0 9 | -18

0 -1.33 | 2.67

divide the second row by 9:

1 -1.67 | 6.33

0 1 | -2

0 -1.33 | 2.67

multiply the second row by 1.33 and add it to the third row and it remains:

1 -1.67 | 6.33

0 1 | -2

0 0 | 0

multiply the second row by 1.67 and add it to the first row and we have:

1 0 | 3

0 1 | -2

0 0 | 0

Therefore, from here we can deduce that x = 3 and y = -2

Mathematics

Solves a systems of linear equations in two variables. Solve the following systems by graphing 1) 2x + y = 5 and x-3y = - 8 2) 6x - 3y = - 9 and 2x + 2y = -6 Solve the following systems by substitution 3) y = 5x-3 and -x - 5y = - 11 4) 2x - 6y = 24 and x - 5y - 22 Solve the following systems by elimination 5) - 4x - 2y = -2 and 4x + 8y = -24 6) x - y = 11 and 2x + y = 19

Step-by-step answer

P Answered by PhD

Linear equations are represented by straight lines.

Graphs

(1) 2x + y = 5 and x - 3y = -8

See attachment for the graphs of 2x + y = 5 and x - 3y = -8

From the graph, we have:

(x,y) = (1,3)

(2) 6x - 3y = -9 and 2x + 2y = -6

See attachment for the graphs of 6x - 3y = -9 and 2x + 2y = -6

From the graph, we have:

(x,y) = (-2,-1)

Substitution

3) y = 5x-3 and -x - 5y = - 11

Make x the subject in $\mathbf{-x - 5y = -11}$

$\mathbf{x= 11 - 5y}$

Substitute $\mathbf{x= 11 - 5y}$ in $\mathbf{y = 5x - 3}$

$\mathbf{y = 5(11 - 5y) - 3}$

Open bracket

$\mathbf{y = 55 - 25y - 3}$

Collect like terms

$\mathbf{y +25y= 55 - 3}$

$\mathbf{26y= 52}$

Divide both sides by 2

$\mathbf{y= 2}$

Substitute $\mathbf{y= 2}$ in $\mathbf{x= 11 - 5y}$

$\mathbf{x =11 - 5(2)}$

$\mathbf{x =1}$

So, the solution is (x,y) = (1,2)

4) 2x - 6y = 24 and x - 5y = 22

Make x the subject in $\mathbf{x - 5y = 22}$

$\mathbf{x = 5y + 22}$

Substitute $\mathbf{x = 5y + 22}$ in $\mathbf{2x - 6y =24}$

$\mathbf{2(5y + 22) - 6y =24}$

$\mathbf{10y + 44 - 6y =24}$

Collect like terms

$\mathbf{10y - 6y =24 - 44}$

$\mathbf{4y =- 20}$

Divide by 4

$\mathbf{y =- 5}$

Substitute $\mathbf{y =- 5}$ in $\mathbf{x = 5y + 22}$

$\mathbf{x = 5(-5) + 22}$

$\mathbf{x = -3}$

So, the solution is (x,y) = (-3,-5)

Elimination

5) - 4x - 2y = -2 and 4x + 8y = -24

Add both equations to eliminate x

$\mathbf{-4x + 4x - 2y + 8y = -2- 24}$

$\mathbf{6y = -26}$

Divide both sides by 6

$\mathbf{y = -\frac{13}{3}}$

Substitute $\mathbf{y = -\frac{13}{3}}$ in $\mathbf{4x + 8y = -24}$

$\mathbf{4x - 8 \times \frac{13}{3} = -24}$

$\mathbf{4x - \frac{104}{3} = -24}$

Collect like terms

$\mathbf{4x = \frac{104}{3} -24}$

$\mathbf{4x = \frac{104-72}{3} }$

$\mathbf{4x = \frac{32}{3} }$

Divide both sides by 4

$\mathbf{x = \frac{8}{3} }$

Hence, the solution is (x,y) = (8/3,-13/3)

6) x - y = 11 and 2x + y = 19

Add both equations to eliminate y

$\mathbf{x + 2x - y + y = 11 +19}$

$\mathbf{3x = 30}$

Divide through by 3

$\mathbf{x = 10}$

Substitute $\mathbf{x = 10}$ in $\mathbf{x - y = 11}$

$\mathbf{10 - y = 11}$

Collect like terms

$\mathbf{ y =10 - 11}$

$\mathbf{ y =- 1}$

Hence, the solution is (x,y) = (10,-1)

Read more about linear equations at:

link

Solves a systems of linear equations in two variables.

Solve the following systems by graphing1) 2x

Mathematics

Step-by-step answer

P Answered by PhD

Linear equations are represented by straight lines.

Graphs

(1) 2x + y = 5 and x - 3y = -8

See attachment for the graphs of 2x + y = 5 and x - 3y = -8

From the graph, we have:

(x,y) = (1,3)

(2) 6x - 3y = -9 and 2x + 2y = -6

See attachment for the graphs of 6x - 3y = -9 and 2x + 2y = -6

From the graph, we have:

(x,y) = (-2,-1)

Substitution

3) y = 5x-3 and -x - 5y = - 11

Make x the subject in $\mathbf{-x - 5y = -11}$

$\mathbf{x= 11 - 5y}$

Substitute $\mathbf{x= 11 - 5y}$ in $\mathbf{y = 5x - 3}$

$\mathbf{y = 5(11 - 5y) - 3}$

Open bracket

$\mathbf{y = 55 - 25y - 3}$

Collect like terms

$\mathbf{y +25y= 55 - 3}$

$\mathbf{26y= 52}$

Divide both sides by 2

$\mathbf{y= 2}$

Substitute $\mathbf{y= 2}$ in $\mathbf{x= 11 - 5y}$

$\mathbf{x =11 - 5(2)}$

$\mathbf{x =1}$

So, the solution is (x,y) = (1,2)

4) 2x - 6y = 24 and x - 5y = 22

Make x the subject in $\mathbf{x - 5y = 22}$

$\mathbf{x = 5y + 22}$

Substitute $\mathbf{x = 5y + 22}$ in $\mathbf{2x - 6y =24}$

$\mathbf{2(5y + 22) - 6y =24}$

$\mathbf{10y + 44 - 6y =24}$

Collect like terms

$\mathbf{10y - 6y =24 - 44}$

$\mathbf{4y =- 20}$

Divide by 4

$\mathbf{y =- 5}$

Substitute $\mathbf{y =- 5}$ in $\mathbf{x = 5y + 22}$

$\mathbf{x = 5(-5) + 22}$

$\mathbf{x = -3}$

So, the solution is (x,y) = (-3,-5)

Elimination

5) - 4x - 2y = -2 and 4x + 8y = -24

Add both equations to eliminate x

$\mathbf{-4x + 4x - 2y + 8y = -2- 24}$

$\mathbf{6y = -26}$

Divide both sides by 6

$\mathbf{y = -\frac{13}{3}}$

Substitute $\mathbf{y = -\frac{13}{3}}$ in $\mathbf{4x + 8y = -24}$

$\mathbf{4x - 8 \times \frac{13}{3} = -24}$

$\mathbf{4x - \frac{104}{3} = -24}$

Collect like terms

$\mathbf{4x = \frac{104}{3} -24}$

$\mathbf{4x = \frac{104-72}{3} }$

$\mathbf{4x = \frac{32}{3} }$

Divide both sides by 4

$\mathbf{x = \frac{8}{3} }$

Hence, the solution is (x,y) = (8/3,-13/3)

6) x - y = 11 and 2x + y = 19

Add both equations to eliminate y

$\mathbf{x + 2x - y + y = 11 +19}$

$\mathbf{3x = 30}$

Divide through by 3

$\mathbf{x = 10}$

Substitute $\mathbf{x = 10}$ in $\mathbf{x - y = 11}$

$\mathbf{10 - y = 11}$

Collect like terms

$\mathbf{ y =10 - 11}$

$\mathbf{ y =- 1}$

Hence, the solution is (x,y) = (10,-1)

Read more about linear equations at:

link

Mathematics

System of equations elimination method 1. -3x+10y=11, -8x+2y=-20 2. 4x+16y=-19, -8x+2y=10 3. 2x+6y=-2, -x+2y=6 4. -8x-y=-13, 5x-3y=-10 5. -4x+6y=4, -x+8y=1 6. -x+y=-5, 7x-3y=23 7. -9x-5y=26, 4x-4y=-24

Step-by-step answer

P Answered by Specialist

1. x = 3, y = 2
2. x = -99/68, y = -14/17
3. x = -4, y = 1
4. x = 1, y = 5
5. x = -1, y = 0
6. x = 2, y = -3
7. x = 14, y = 20

I attached the pictures with the work.
System of equations elimination method 1. -3x+10y=11, -8x+2y=-20 2. 4x+16y=-19, -8x+2y=10 3. 2x+6y=-

System of equations elimination method 1. -3x+10y=11, -8x+2y=-20 2. 4x+16y=-19, -8x+2y=10 3. 2x+6y=-

Mathematics

Step-by-step answer

P Answered by Specialist

Mathematics

Which solution method, graphing, substitution, or elimination is the most appropriate for solving each system of equations? explain. 1. 3x + 8y = -4 2x - 4y = 16 2. x + y = 19 3x - 2y = -3

Step-by-step answer

P Answered by Master

Ok from my math knowledge here is what I believe is the answer for each of these:

1) elimination: because you can just multiply the bottom equation (both sides of it!) by 2, and so eliminate the y variable. and from there it's easy to solve for x, and then you can use the answer for x to find y by substitution into one of the equations.

2) substitution: because you can see that it's easy to solve for either x OR y. and once you have the equation for either x= something or y= something you can just substitute that into one of the equations.

Mathematics

Which solution method, graphing, substitution, or elimination is the most appropriate for solving each system of equations? explain. 1. 3x + 8y = -4 2x - 4y = 16 2. x + y = 19 3x - 2y = -3

Step-by-step answer

P Answered by Specialist

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