Question

How do you solve `x + 4y = -1` and `2x - y = 7`?

Answer 1

The lines intersect at the point `(3,-1)`.

Refer to the explanation for the process.

Explanation:

Solve system of equations

Equation 1: `x+4y=-1`

Equation 2: `2x-y=7`

Both equations are linear equations in standard form:

`Ax+By=C`.

The point `(x,y)` which results from solving the system is the point of intersection between the two lines.

I will use the substitution method to solve the system.

Solve Equation 1 for `x`.

`x+4y=-1`

Subtract `4y` from both sides of the equation.

`x=-4y-1`

Substitute `-4y-1` for `y` in Equation 2.

`2x-y=7`

`2(-4y-1)-y=7`

Expand.

`-8y-2-y=7`

Add `2` to both sides.

`-8y-y=7+2`

Simplify.

`-9y=9`

Divide both sides by `-9`.

`y=9/(-9)`

Simplify.

`y=-1`

To solve for `x`, substitute `-1` for `y` in Equation 1.

`x+4y=-1`

`x+4(-1)=-1`

Simplify.

`x-4=-1`

Add `4` to both sides.

`x=-1+4`

`x=3`

The point of intersection between the two lines is `(3,-1)`.

graph{(4y+x+1)(-y+2x-7)=0 [-10, 10, -5, 5]}