Given the system of linear equations.

-x + y = 5, 4x + 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.

You can solve for y in equation one, then substitute that answer into equation two.

-x+y=5

add x to both sides to solve for y. The x's cancel each other out on the left side of the equation.

y=5+x

Now substitute that answer in the second equation.

4x+y=10

4x + (5+x) = 10

5x+5=10

Subtract 5 from both sides

5x=5

Divide both sides by 5 to solve for x

x=1

Substitute that answer in equation one to now solve for y.

-x+y=5

-1+y=5

Add one to both sides

y=6

Use those answers to check if they work in the given equations.

-1+6=5 yes

4 (1) + 6=10 yes