11.03.2020

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

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09.07.2023, solved by verified expert
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Solve using elimination. x − 8y = 19 9x + 8y, №18010880, 11.03.2020 04:09

Step-by-step explanation:

Let's add together the two equations

Solve using elimination. x − 8y = 19 9x + 8y, №18010880, 11.03.2020 04:09

At this point I would recommend simply using the value of x in the firs equation to find y. Solve using elimination. x − 8y = 19 9x + 8y, №18010880, 11.03.2020 04:09

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

Solve using elimination. x − 8y = 19 9x + 8y, №18010880, 11.03.2020 04:09

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Mathematics
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
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.


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


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


Solves a systems of linear equations in two variables.

Solve the following systems by graphing1) 2x
Solves a systems of linear equations in two variables.

Solve the following systems by graphing1) 2x
Mathematics
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
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 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
Step-by-step answer
P Answered by Specialist
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.

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