Solve the system y = -x + 7 and y = 0.5(x - 3)^2

Question

asked Jan 15, 2020 134k views

2 Answers

Darian Moody · Answer 1 · 2020-01-21T11:32:51+0000

Answer:

$x=-1;\ y=8\\x=5;\ y=2$

Explanation:

You can make both equations equal and solve for the variable x, as you can see below:

-x+7=0.5(x-3)^2

Keep on mind that:

(a-b)^2=a^2-2ab+b^2

Then:

$-x+7=0.5(x-3)^2\\-x+7=0.5(x^2-2(x)(3)+3^2)\\-x+7=0.5x^(2)-3x+4.5\\0=0.5x^2-2x-2.5$

Apply the quadratic formula:

$x=(-b+/-√(b^2-4ac))/(2a)\\\\x=(-(-2)+/-√((-2)^2-4(0.5)(-2.5)))/(2(0.5))\\x=-1\\x=5$

Substitute each value into one of the originl equations to find y, then:

$y=-(-1)+7=8\\y=-5+7=2$