Answer:
(2,6) and (-1,3)
Step-by-step explanation:
Hi there!
We're given the system of equations:
y=x+4
y=x²+2
and we need to solve the system
You may first notice that both equations are equal to y, so we can set them to equal each other via a property known as transitivity (if a=b and b=c, then a=c)
x²+2=x+4
subtract x from both sides
x²-x+2=4
subtract 4 from both sides
x²-x-2=0
we can factor the polynomial
the numbers that add up to -1 and multiply to get -2 are -2 and 1
(x-2)(x+1)=0
solve
x=2, x=-1
both values of x work- so we'll have 2 solutions in this case
now we need to solve for y; we can do this by substituting the value of x into one of the equations to solve for y
let's use y=x+4
so if we'll use x=2,
y=2+4
y=6
one solution will be (2,6)
and if we use x=-1
y=-1+4
y=3
and the other will be (-1,3)
Hope this helps! :)
