Question

Use the following system of linear equations to do Part A and Part B below.
{- x + y = 5
{4 x + y = 10

Part A: Use substitution to find the solution to the systems of equations. Include all of your work in your final answer.

Part B: Algebraically verify your answer to Part A. Include all of your work in your final answer.


WRITER

Answer 1

Part A — Substitution

1. From the first equation, -x + y = 5, solve for y:
y = x + 5.

2. Substitute y = x + 5 into the second equation, 4x + y = 10:
4x + (x + 5) = 10
5x + 5 = 10
5x = 5
x = 1.

3. Find y using y = x + 5:
y = 1 + 5 = 6.

Solution: (x, y) = (1, 6).

Part B — Algebraic verification

Substitute x = 1 and y = 6 into each original equation:

- For -x + y = 5:
-1 + 6 = 5 ✓

- For 4x + y = 10:
4(1) + 6 = 4 + 6 = 10 ✓

Both equations are satisfied, so (1, 6) is the correct solution.