Y = 3x y = 1/2x Find by using systems of equation by elimination.

A. One solution
B. No Solution
C. Infinitely Many Solutions

Step-by-step explanation:

y = 3x + 0

y = 1/2x + 0

y = 3x + 0

-3x  -3x

y - 3x = 0

y = 1/2x + 0

2(y = 1/2x + 0)

2y = x + 0

-x     -x

2y - x = 0

y - 3x = 0

2y - x = 0

1(y - 3x = 0)    = y = - 3x = 0

-3(2y - x = 0)  = -6y + 3x = 0

y = - 3x = 0

-6y + 3x = 0

-5y = 0

/-5     /-5

y = 0

y = 3x + 0

0 = 3x + 0

-3x   -3x

-3x + 0 = 0

      - 0   -0

-3x = 0

/-3   /-3

x = 0

(x,y) -> (0, 0)

Hope this helps!

1. Independent

2. (4, -1)

3. (4, 3)

4. (2,5)

5. (2, -1)

6. (10, -1)

7. (2, -3)

8. (1/3, 2/3)

9. 4 and 3

10. (4,-1)

Step-by-step explanation:

1.If a system has one or more solution then it is called Consistent system.

If a system has no solution then it is called an Inconsistent system.

If Consistent system has exactly one solution then it is called Dependent

and If the Consistent system has an infinite number of the solution then it is called Independent.

Therefore, If a system has exactly one solution it is called Dependent.

2. The equations we have:

y = -x + 3 and y = -+3

After solving these equations, We get, x = 4, y = -1

3. The substitution method is we substitute the value of x or y from one equation to another equation and solve them.

After solving given equations. We get,

x = 4, y = 3

4. Similarly, We solve both equations, we get

x = 2, y = 5

5. In the Elimination method, firstly we equate either coefficient of x or y in both equations (if either coefficient of x or y is not equal) after that we add or subtract both equations to eliminate one variable and solve them.

After solving given equations. We get,

x = 2, y = -1

9. We get equations,

x+y=7 and 4(7-y) = 5y+1

After solving these we get the value of x and y.

10. The point of intersection is the solution of both equations. Here we see the point of intersection is (4, -1)

2) A

3) B

4) C

5) A

6) C

Step-by-step explanation:

2) Lets add 2 equation together, we will find:

If we put y value in the first equation:

It is A

3) Substation is the best way to solve the system.

Lets multiply first equation with 4:

Substitute 2x with 4y:

and x=8

4) Again lets substitute 3x with -y:

Therefore x=-2

Correct answer is C

5) None of real numbers is the solution of this system.

6) First lets multiply first equation with -1 and add equations together:

It falls to III

The answer is C

1. Independent

2. (4, -1)

3. (4, 3)

4. (2,5)

5. (2, -1)

6. (10, -1)

7. (2, -3)

8. (1/3, 2/3)

9. 4 and 3

10. (4,-1)

Step-by-step explanation:

1.If a system has one or more solution then it is called Consistent system.

If a system has no solution then it is called an Inconsistent system.

If Consistent system has exactly one solution then it is called Dependent

and If the Consistent system has an infinite number of the solution then it is called Independent.

Therefore, If a system has exactly one solution it is called Dependent.

2. The equations we have:

y = -x + 3 and y = -+3

After solving these equations, We get, x = 4, y = -1

3. The substitution method is we substitute the value of x or y from one equation to another equation and solve them.

After solving given equations. We get,

x = 4, y = 3

4. Similarly, We solve both equations, we get

x = 2, y = 5

5. In the Elimination method, firstly we equate either coefficient of x or y in both equations (if either coefficient of x or y is not equal) after that we add or subtract both equations to eliminate one variable and solve them.

After solving given equations. We get,

x = 2, y = -1

9. We get equations,

x+y=7 and 4(7-y) = 5y+1

After solving these we get the value of x and y.

10. The point of intersection is the solution of both equations. Here we see the point of intersection is (4, -1)

2) A

3) B

4) C

5) A

6) C

Step-by-step explanation:

2) Lets add 2 equation together, we will find:

If we put y value in the first equation:

It is A

3) Substation is the best way to solve the system.

Lets multiply first equation with 4:

Substitute 2x with 4y:

and x=8

4) Again lets substitute 3x with -y:

Therefore x=-2

Correct answer is C

5) None of real numbers is the solution of this system.

6) First lets multiply first equation with -1 and add equations together:

It falls to III

The answer is C

1) (-6,-9)

times the top equation buy -4 so you cancel out the y

so it be -8x+4y=12 no cancel out the y's

so it be -8x=12 and 5x=6

now combined like terms to get -3x= 36

x = -6 now go plug that back in one of the equations to get y

y = -9

2) (-2,-5)

now on this one you going to substitute y= (2x-1) for y in the otheir eqaution

so it look like 3x-(2x-1)=-1

do your combining of like terms and your division & you get x = -2

now plug x in to y=2x-1 to get y = -5

The value of the variable x is -2 and the value of the variable y is -7.

Step-by-step explanation:

The substitution method consists of:

In this case,  you have the system of equations:

Isolating the variable y from the second equation:

y= -1 +3*x

Replacing this expression in the first equation:

2*x-3*( -1 +3*x)= 17

Solving:

2*x -3*(-1)-3*3*x= 17

2*x +3 -9*x= 17

2*x -9*x= 17 -3

(-7)*x= 14

x= 14÷(-7)

x= -2

Now, replacing the value of x in the expression y = -1 + 3 * x you get:

y= -1 +3*(-2)

Solving:

y= -1 -6

y= -7

So, the value of the variable x is -2 and the value of the variable y is -7.

The value of the variable x is -2 and the value of the variable y is -7.

Step-by-step explanation:

The substitution method consists of:

In this case,  you have the system of equations:

Isolating the variable y from the second equation:

y= -1 +3*x

Replacing this expression in the first equation:

2*x-3*( -1 +3*x)= 17

Solving:

2*x -3*(-1)-3*3*x= 17

2*x +3 -9*x= 17

2*x -9*x= 17 -3

(-7)*x= 14

x= 14÷(-7)

x= -2

Now, replacing the value of x in the expression y = -1 + 3 * x you get:

y= -1 +3*(-2)

Solving:

y= -1 -6

y= -7

So, the value of the variable x is -2 and the value of the variable y is -7.