Question

Solve the system using elimination y=-3x+6 y=x^2-4

Answer 1

Mutiply first equation by -1 and add to 2nd

-y=3x-6
y=x^2-4 +
0=x^2+3x-10
factor like any equation
what 2 numbers multiply to -10 and add to 3
-2 and 5
0=(x-2)(x+5)
set to zero
x-2=0
x=2

x+5=0
x=-5
solve for y in each case

for x=2
y=2^2-4
y=4-4
y=0
(2,0) is a point

for x=-5
y=(-5)^2-4
y=25-4
y=21
(-5,21) is another



the solutions are
(2,0) and
(-5,21)