Question

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

Answer 1

The point of intersection is `(-1,1)`.

Explanation:

Solve system:

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

`color(green)("Equation 2:"` `3x-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 `(x,y)` is the point of intersection between the lines.

Solve Equation 1 for `x`.

`-x-2y=-1`

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

`-x=2y-1`

Multiply both sides by `-1`.

`x=-2y+1=`

`x=color(red)(1-2y`

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

`3(color(red)(1-2y))-y=-4`

Expand.

`3-6y-y=-4`

Subtract `3` from both sides.

`-6y-y=-4-3`

Simplify.

`-7y=-7`

Divide both sides by `-7`.

`y=(color(red)cancel(color(black)(-7)))^1/(color(red)cancel(color(black)(-7)))^1`

`y=color(teal)1`

Substitute `color(teal)1` for `y` in Equation 1.

`-x-2(color(teal)(1))=-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 : `(-1,1)`

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