Question

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

Answer 1

Answer:

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

Step-by-step 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:

$x=\frac{-b+/-\sqrt{b^2-4ac}}{2a}\\\\x=\frac{-(-2)+/-\sqrt{(-2)^2-4(0.5)(-2.5)}}{2(0.5)}\\x=-1\\x=5$

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

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