Solve by the elimination method

7x-y=17
x+7y=31

What is the solution of the system?

multiply the fist equation by 7

49x - 7y = 119
add the second
x + 7y = 31

50x = 150
x = 3

sub that into the second equation ....

you finish it, let me know what you got.

To solve the system of equations using the elimination method, we need to eliminate one variable by adding or subtracting the two equations. Let's solve the system step-by-step:

1. Multiply the first equation by 7 to make the coefficients of the x-terms the same:
(7)(7x - y) = (7)(17)
49x - 7y = 119 ----(Equation 1)

2. Now, we can add Equation 1 and Equation 2:
(49x - 7y) + (x + 7y) = 119 + 31
49x + x - 7y + 7y = 150
50x = 150

3. Divide Equation 3 by 50 to solve for x:
x = 150/50
x = 3

4. Substitute the value of x into either Equation 1 or Equation 2 to find y. Let's use Equation 2:
3 + 7y = 31
7y = 31 - 3
7y = 28

5. Divide Equation 5 by 7 to solve for y:
y = 28/7
y = 4

So, the solution to the system of equations is x = 3 and y = 4.