Question

Find the solution of the system of equations.

Answer
-x + 4y = 25
-2x - 2y = -10
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Answer 1

x = - 1, y = 6

Explanation:

To solve this system of equations we will first eliminate one of the variables in the system, solve for the other variable, then substitute the value of that solved variable into one of the equations to solve for the remaining variable

We have the following equations:
- x + 4y = 25 which can be written as
- 1x + 4y = 25 ... (1)

- 2x -2y = - 10.....(2)

• Make one of the coefficients of x or y the same in both equations and subtract/add to eliminate that variable from both equations:
  Multiply equation (2) by 2:
  ==> 2(-2x - 2y) = 2 (-10)
  ==> - 4x - 4y = -20 ... (3)
  
• Add equations (1) and (3) to eliminate y
  - 1x + 4y = 25
  +
  -4x - 4y = -20
  --------------------
  -5x + 0 = 5

==> -5x = 5
==> x = 5/-5 = -1

• Substitute x = -1 into equation (1)
  -1x + 4y = 25 becomes -
  -1(-1) + 4y = 25
  1 + 4y = 25
  4y = 25 - 1 = 24
  y = 24/4 = 6

So the solution set is
x = -1, y = 6