Question

Is (

–
2,
–
3) a solution to this system of equations?
y=
–
5x–13
y=x–1

Answer 1

No, (2,3) is not a solution.

Explanation:

`y=5x-13\\y=x-1\\\\x=y+1\\y=5(y+1)-13\\y=5y+5-13\\y=5y-8\\4y=8\\y=2`

Insert y=2 into y=5x-13:

`(2)=5x-13\\2+13=5x\\15=5x\\x=3`

This means the solution is (3,2). Therefore, (2,3) is not a solution to this system of equations. This answer can be confirmed by substituting the given values into the equations:

`x=2\\y=3\\\\(3)=5(2)-13\\3\\eq-3\\\\(3)=(2)-1\\3\\eq1`