Question

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

Answer 1

The solutions are (-1,8) and (5,2).

Explanation:

Answer 2

`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`