Question

How do you solve the system of equations `y= \frac { - 3} { 4} x - 4` and `y = \frac { 8} { 9} x - \frac { 4} { 5}`?

Answer 1

`(-576/295, -748/295)`

Explanation:

Given: `y = -3/4x - 4 " and " y = 8/9 x - 4/5`

Since the solution to the equation is the intersection point of the two lines, a point that that both lines share, set the two `y`-values equation and solve for `x`:

`-3/4x - 4 = 8/9 x - 4/5`

Get rid of fractions by multiplying the equation by the common denominator (LCM): `4 xx 9 xx 5 = 180`

`180(-3/4x - 4 = 8/9 x - 4/5)`

`-135x - 720 = 160x - 144`

Add `720` to both sides: `" "-135x = 160x +576`

Subtract `160 x` to both sides: `" "-295x = 576`

`x = -576/295`

Substitute `x` into either of the given equations to find `y`:

`y = -3/4 * (-576/295) - 4*295/295`

`y = 432/295 - 1180/295`

`y = -748/295`

CHECK by substituting these values into the 2nd equation:

`-748/295 = 8/9 (-576/295) - 4/5`

`-748/295 = -512/295 - 4/5 * 59/59`

`-748/295 = -512/295 - 236/295`

`-748/295 = -748/295 " "` TRUE

Intersection point is `(-576/295, -748/295)`