Question

How do you solve the system of equations: 4x+3y=7 and -2x+y=9?

Answer 1

The solution for the system of equations is:
`color(blue)(x=-2, y=5`

Explanation:

`color(blue)(4x)+3y=7`............equation `(1)`

`-2x+y=9`, multiplying this equation by `2`
`color(blue)(-4x)+2y=18`......equation `(2)`

Now, we can solve the system of equations through elimination.
Adding the two equations eliminates `color(blue)(4x`

`cancelcolor(blue)(4x)+3y=7`
`cancelcolor(blue)(-4x)+2y=18`

`5y=25`

`color(blue)(y=5`

Now, we find `x` by substituting the value of `y` in equation `1`:

`4x+3y=7`

`4x=7-3y`

`x=(7-3y)/4`

`x=((7-3*5))/4`

`x=((7-15))/4`

`x=-8/4`

`color(blue)(x=-2`