Question

How do you solve 9x -2y = 28 and y= -3x + 1?

Answer 1

`{(x=2), (y = -5) :}`

Explanation:

Your starting system of equations looks like this

`{(9x - 2y = 28), (y = -3x + 1) :}`

Notice that you can rearrange the second equation to get the `x` and `y` terms on the left-hand side of the equation

`{(9x - 2y = 28), (3x + y = 1) :}`

Another thing to notice here is that if you multiply the second equation by `2`, and add the left-hand sides and right-hand sides of the two equations separately, you can cancel out the `y` term.

This will allow you to find the value of `x`.

`{(9x - 2y = 28), (3x + color(white)(x)y = color(white)(x)1 | xx 2) :}`

`{ (9x - 2y = 28), (6x + 2y = color(white)(x)2) :}`

Now add the two equations as described above

`{ (9x - 2y = 28), (6x + 2y = color(white)(x)2) :}`
`color(white)(x)stackrel("-------------------------------")`

`9x - color(red)(cancel(color(black)(2y))) + 6x + color(red)(cancel(color(black)(2y))) = 28 + 2`

`15x = 30 implies x = 30/15 = color(green)(2)`

Now use this value of `x` into one of the two equations to get the value of `y`

`3 * (color(green)(2)) + y = 1`

`y = 1 - 6 = color(green)(-5)`

The solution set for this system of equations will be

`{(x=2), (y = -5) :}`