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

Mar 9, 2018

The lines intersect at the point $\left(3 , - 1\right)$.

Refer to the explanation for the process.

Explanation:

Solve system of equations

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

Equation 2: $2 x - y = 7$

Both equations are linear equations in standard form:

$A x + B y = C$.

The point $\left(x , y\right)$ 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 $x$.

$x + 4 y = - 1$

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

$x = - 4 y - 1$

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

$2 x - y = 7$

$2 \left(- 4 y - 1\right) - y = 7$

Expand.

$- 8 y - 2 - y = 7$

Add $2$ to both sides.

$- 8 y - y = 7 + 2$

Simplify.

$- 9 y = 9$

Divide both sides by $- 9$.

$y = \frac{9}{- 9}$

Simplify.

$y = - 1$

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

$x + 4 y = - 1$

$x + 4 \left(- 1\right) = - 1$

Simplify.

$x - 4 = - 1$

Add $4$ to both sides.

$x = - 1 + 4$

$x = 3$

The point of intersection between the two lines is $\left(3 , - 1\right)$.

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