Answer: (x, y) = ( 2, -3 )
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Explanation:
The first and second equations have 5x and 15x. Note how -3*5x = -15x which helps us get rid of the x terms when we add.
We can multiply both sides of the first equation by -3 to get -15x+6y = -48
An equivalent system of equations is
[tex]\begin{cases}-15x+6y = -48\\15x-7y = 51\end{cases}[/tex]
Add the equations straight down. The x terms add to -15x+15x = 0x = 0, so the x terms go away.
The y terms add to 6y+(-7y) = -1y = -y
The terms on the right hand side add to -48+51 = 3
So we end up with -y = 3 meaning y = -3
This leads to....
5x-2y = 16
5x-2(-3) = 16
5x+6 = 16
5x = 16-6
5x = 10
x = 10/5
x = 2
Or you could use the other equation
15x-7y = 51
15x-7(-3) = 51
15x+21 = 51
15x = 51-21
15x = 30
x = 30/15
x = 2
Either way, we have x = 2 and y = -3 pairing up.
