Question

What is the solution of the system of equations?
y = –3x + 8
y = –5x – 2

A.(23, –5)
B.(–5, 23)
C.(–1.25, 11.75)
D.(3, –17)

Answer 1

first we need to eliminate one of the variables. we can multiply the top by -5 and the bottom by +3 like this

-5(y = -3x+8) = -5y = 15x-40
3(y = -5x-2) = 3y = -15x-6

we do this to eliminate one of the variables let's say y.
and we add both of them together: we notice that x cancels out when we add the two.

-5y = 15x-40
3y = -15x-6

-2y = -46
-2 -2

y = 23

plug this back into the original equation:

23 = -3x+8
-8 -8

15 = -3x
-3 -3

x = -5
y = 23

let's plug these both into the second equation and see what we get:

y = -5x-2

y = -5(-5)-2

-5(-5) = 25 -2 = 23

23 = 23

that's how we know we got it correct

so ( y = 23, and x = -5)