solve the system of equations

Question

y=2x

y=x^2-8

Answer 1

x=4 or -2

y=2x =8 or -4

solutions are (4,8) and (-2,-4)

y=x²-8 y=16-8=8 for x=4

y=4-(-4)=8 for x=4

Mr. K's answer gives the calculations for x. I just added some for finding the corresponding y values

and check the answer to see if it fits the original equations.

Another way to do this is graph the 2 equations and see where they intersect. You have straight line intersecting a parabola, so you expect 2 possible answers, 2 points where there are intersections

y=x²-8 is a parabola with y intersection of -8 (set x=0 and solve for y)

set y=0 and solve for x gives the x-intercepts, where the parabola crosses the x-axis

that's the square root of 8 or 2(2)^1/2 = 2(1.414)= 2.828 = almost 3

the straight line, y=2x goes through the origin with slope of 2. it cuts or intersects the parabola once in the first quadrant and once in the third quadrant. Just a rough sketch shows the intersections are about

(4,8) and (-2,-4). The parabola is symmetric about the y axis with vertex at y=-8

Answer 2

y = 2x..........(1)

y = x² - 8.....(2)

So, first notice that you can take equation (1) and substitute it into equation (2) as follows:

2x = x² - 8 <--------This is because equation (1) told you that 2x is y.

Now move everything to one side (since this is a quadratic equation) and set the other side to zero.

0 = x² - 2x - 8

(and factor)

0 = (x - 4)(x + 2)

Hence,

x - 4 = 0 or x + 2 = 0 <-------Zero Product Property

x = 4, or x = -2

*Note: Every quadratic equation that you have to solve must follow the following steps:

1) Move everything to one side and set one side to zero.

2) Factor - If you need help on factoring, you can find plenty of help here on Wyzant, or you can search up youtube videos (there are thousands of them on factoring)

3) Solve for x using the zero product property

Hope this helps

Mr. K