Question

How do you solve the system of equations `3x-3y=-9` and `3x-5y=-29` by combining the equations?

Answer 1

The easiest way to solve these equations is to subtract the two equations, this eliminating one of the variables ( `x`) and then solving for the other variable (`y`)

`x=7 and y =10`

Explanation:

`+ 3x -( + 3x) = 0` so if the two equations are subtracted, the `x` term disappears.

`" "3x - 3y = -9`
`-3x - (-5y) = -( - 29)" "` This gives:

`0x + 2y = + 20" "` next solve for y by dividing both sides by 2

`(2y)/2 = 20/2" "` This gives :

`y = 10`

Next substitute `y =10`into either of the equation and solve for `x`.

`3x + (-3 )xx 10 = -9` This gives

`3x -30 = -9 " "` Add 30 to both sides giving

`3x - 30 +30 = -9 +30" "` which gives

`3x = + 21" "` Finally divide both sides by 3

`(3x)/3 = 21/3` The answer is

`x = 7`

To make sure the answer is correct, substitute the values for`x and y` into the other equation to check the answer:

`3x -5y =-29`

`3 xx 7 - 5 xx 10 = - 29" "` this gives

`+ 21 -50 = -29" "` adding the integers gives

`-29 = -29" "` The answer checks.