# How do you solve the following system?: -x -2y =-1, 3x -y = -4

Mar 2, 2018

The point of intersection is $\left(- 1 , 1\right)$.

#### Explanation:

Solve system:

color(blue)("Equation 1:" $- x - 2 y = - 1$

color(green)("Equation 2:" $3 x - y = - 4$

The given equations are linear equation in standard form. I will show how to solve this system of equations using substitution. The resulting point $\left(x , y\right)$ is the point of intersection between the lines.

Solve Equation 1 for $x$.

$- x - 2 y = - 1$

Subtract $2 y$ from both sides of the equation.

$- x = 2 y - 1$

Multiply both sides by $- 1$.

$x = - 2 y + 1 =$

x=color(red)(1-2y

Substitute color(red)(1-2y for $x$ in Equation 2 and solve for $y$.

$3 \left(\textcolor{red}{1 - 2 y}\right) - y = - 4$

Expand.

$3 - 6 y - y = - 4$

Subtract $3$ from both sides.

$- 6 y - y = - 4 - 3$

Simplify.

$- 7 y = - 7$

Divide both sides by $- 7$.

$y = {\left(\textcolor{red}{\cancel{\textcolor{b l a c k}{- 7}}}\right)}^{1} / {\left(\textcolor{red}{\cancel{\textcolor{b l a c k}{- 7}}}\right)}^{1}$

$y = \textcolor{t e a l}{1}$

Substitute $\textcolor{t e a l}{1}$ for $y$ in Equation 1.

$- x - 2 \left(\textcolor{t e a l}{1}\right) = - 1$

Simplify.

$- x - 2 = - 1$

Add $2$ to both sides.

$- x = - 1 + 2$

Simplify.

$- x = 1$

Multiply both sides by $- 1$.

$x = - 1$

Point of intersection : $\left(- 1 , 1\right)$

graph{(-2y-x+1)(-y+3x+4)=0 [-10, 10, -5, 5]}