Question

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.

Answer 1

(1,6)

Explanation:

To solve by substitution, rearrange -x+y=5 to y=x+5 and substitute it into 4x+y=10.

4x + (x+5) = 10

4x+x+5=10

5x+5=10

5x=5

x=1

Now substitute x = 1 back in to find y.

y= (1) + 5

y=6

Solution is (1,6)

Verify substituting both values into each equation in to verify true.

-x+y=5

-(1)+6 = 5

-1+6=5

5=5 True

4(1)+6=10

4+6=10

10=10 True

Answer 2

(1,6)

Explanation:

To solve by substitution, rearrange -x+y=5 to y=x+5 and substitute it into 4x+y=10.

4x + (x+5) = 10

4x+x+5=10

5x+5=10

5x=5

x=1

Now substitute x = 1 back in to find y.

y= (1) + 5

y=6

Solution is (1,6)

Verify substituting both values into each equation in to verify true.

-x+y=5

-(1)+6 = 5

-1+6=5

5=5 True

4(1)+6=10

4+6=10

10=10 True