Question

Use the linear combination method to solve the system of equations. Justify each step of your solution. If steps are not explained, you will not receive credit for that step.
-3x - 7y = -28
2x + 3y = 7

Answer 1

Answer:

Step-by-step explanation:

The given system of equations is expressed as

-3x - 7y = -28 - - - - - - - - - - - - 1

2x + 3y = 7 - - - - - - - - - - - - - - 2

We would eliminate x by multiplying equation 1 by 2 and equation 2 by 3. It becomes

- 6x - 14y = - 56- - - - - - - - - - - 3

6x + 9y = 21 - - - - - - - - - - - 4

Adding equation 3 to equation 4, it becomes

- 5y = - 35

Dividing the left hand side and the right hand side of the equation by - 5, it becomes

- 5y/- 5 = - 35/- 5

y = 7

Substituting y = 7 into equation 2, it becomes

2x + 3 × 7 = 7

2x + 21 = 7

Subtracting 21 from the left hand side and the right hand side of the equation, it becomes

2x + 21 - 21 = 7 - 21

2x = - 14

Dividing the left hand side and the right hand side of the equation by 2, it becomes

2x/2 = - 14/2

x = - 7

Answer 2

Answer:

y=7

x=-7

Step-by-step explanation:

2(-3x - 7y )= 2(-28)

3(2x+ 3y)=3(7)

-6x - 14y = -56

6x + 9y = 21

Add the two equations

-1(0x - 5y)= -1(- 35)

5y = 35

Divide both sides by 5

y=7

Substitution

6x + 9(7) = 21

6x + 63 = 21

Subtract 63 from both sides

6x = -42

Divide both sides by 6

x= - 7