Solve the linear system.

Question

Enter your answer as an ordered pair.

2x + 3y = 31

y = x + 7

Answer 1

Solve the system of equations

2x + 3y = 31

y = x + 7

SOLUTION:

2x + 3y = 31

2x + 3(x+7) = 31

2x + 3x + 21 = 31

5x = 10

x = 2

y = x + 7

y = 2 + 7

y = 9

Solution: (x,y) = (2, 9)

Answer 2

In order to solve this linear system of equations, we first need to solve for either the x or y variable. In that case, I will choose to first solve for the x variable.

I will solve for the x variable by multiplying the bottom equation by 3 and then subtracting the equations:

2x + 3y = 31

(-x + y = 7)(3)

2x + 3y = 31

- (-3x + 3y = 21)

= 5x = 10

x = 2

Now we plug x = 2 back into either one of the original equations:

2(2) + 3y = 31

3y = 27

y = 9

Therefore, the solution in ordered pair form is (2,9)