Question

IN DESPERATE NEED OF HELP :(

4x - 9y =9


-x + 3y = 6



Rewrite one of the two equations above in the form ax + by = c, where a, b, and c are constants, so that the sum of the new equation and the unchanged equation from the original system results in an equation in one variable.

Answer 1

So, the problem is asking for one of the equations to be rewritten. Lets rewrite the second one. The way to create a system of equations that will cancel is to create a situation where the a or b of both equations add to 0. In this case, we can multiply the second equation by 3 to turn the 3y into 9y.

`3(-x + 3y) = (6)3`

`-3x + 9y = 18`

Our new system is
`4x - 9y =9` and
`-3x + 9y = 18`. We can now add these together.

`4x - 9y = 9`

`-3x + 9y = 18`

Adding each part straight down, we get the equation:

`x + 0 = 27`

We now have an equation with a single variable, which also tells us that x is equal to 27.

Extra: To find the value of y after this, we merely need to plug in the value of x to one of the equations and solve for y.

`-27 + 3y = 6`

`3y = 33`

`y = 11`