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Solve the following system by substitution. CHECK the solution.

3y = 2x + 12
y + 3x = -7

1 Answer

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We can use substitution to solve this system of equations. We can solve the first equation for y and get:

y = (2x + 12)/3

We can then substitute this expression for y into the second equation:

(2x + 12)/3 + 3x = -7

Multiplying both sides of this equation by 3 to eliminate the denominator, we get:

2x + 12 + 9x = -21

Simplifying this equation gives:

11x = -33

Dividing both sides by 11, we get:

x = -3

We can then substitute this value of x back into either of the two original equations to find y. Using the first equation, we get:

3y = 2(-3) + 12

3y = 6

y = 2

Therefore, the solution to the system of equations is x = -3 and y = 2.

To check the solution, we substitute these values back into both equations:

3y = 2x + 12 3(2) = 2(-3) + 12 6 = 6

This equation is true, so the solution (x = -3, y = 2) checks out.

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