Question

How do you solve the system of equations `-\frac { 3} { 4} x - \frac { 1} { 2}y = -2` and `x-y=6`?

Answer 1

After multiplying first equation with `-4` and second on with `2`,

`-4*(-3/4*x-1/2*y)+2*(x-y)=(-4)*(-2)+6*2`

`3x+2y+2x-2y=8+12`

`5x=20`

`x=4`

After plugging `x` into second one, I found `4-y=6` or `y=-2`

Explanation:

1) I multiplied first equation with `-4` and second on with `2` for removing `y` term.

2) I found `x`

3) I plugged `x` into second one for finding `y`

Answer 2

The point of intersection is `(4,-2)`.

Refer to the explanation for the process.

Explanation:

Solve system:

Equation 1: `color(blue)(-3/4x-1/2y=-2`

Equation 2: `color(red)(x-y=6`.

These are linear equations in standard form. The point `(x,y)` represents the point of intersection between the two lines.These equations will be solved simultaneously by substitution.

Start with Equation 2 because it is very simple. Solve for `x`.

`x=6+y`

Substitute `6+y` for `x` in Equation 1:

`-3/4(6+y)-1/2y=-2`

Simplify `1/2y` to `y/2`.

`(-3(6+y))/4-y/2=-2`

Multiply both sides by `4`.

`(color(red)cancel(color(black)(4))^1xx-3(6+y))/color(red)cancel(color(black)(4))^(1)-(y)/color(red)cancel(color(black)(2))^1xxcolor(red)cancel(color(black)(4))^2=-2xx4`

Simplify.

`-3(6+y)-2y=-8`

Expand.

`-18-3y-2y=-8`

Add `18` to both sides.

`-3y-2y=-8+18`

Simplify.

`-5y=10`

Divide both sides by `-5`

`y=10/-5`

`y=-2`

Solve for `x`.

Substitute `-2` for `y` in Equation 2 and solve for `x`.

`x-(-2)=6`

Simplify.

`x+2=6`

Subtract `2` from both sides.

`x=6-2`

`x=4`

The point of intersection: `(4,-2)`