Solve the equations, 2x + y = 8 and y = x^2.

Answer 1

The best and easy way to solve this equation is to isolate "y" en both equations and then equal to each other:

y= x^2 . , 2x+y=8 . (2) . . I am going to isolate y by subtracting 2x in both sides.

2x+y =8

-2x . -2x

_________

y=8-2x . (2)

Now y=y

x^2=8-2x

Adding 2x in both sides and subtracting 8 in both sides , we got . x^2+2x-8=0

Factoring: x^2+2x-8=0 . (x . + 4) (x- 2)=0 . two numbers that multiply = -8 . (+4 and -2) and adding = 2

Using the zero property, x+4 =0 . ; x=-4 . , x-2=0 ; x=2

Now that we found "x" , we need to find the value of y in both equations:

when x=2, y=4

like this..... 2x+y=8

2(2) +y=8

4+y=8

-4 . -4

_______

y=4

Therefore : The final answer should be (x,y)=(2,4) .

If graphing calculator is allowed, you can check your answer by graphing and select intersection.

Remember that algebra 1 is the foundation of most math subjects.

Answer 2

Hi.

Your second equation says y=x^2. So you can substitute that in the first equation in order to state everything in terms of the x variable.

2x+y =8

so we can say 2x + x^2 =8 Note that we only substituted the y with x^2

now this would be a quadratic equation: x^2 + 2x -8 = 0

facfor this and you get (x+4)(x-2) = 0

so x=-4 and x=2

if x= -4, y = (-4)^2 = 16

if x= 2, y = (2) ^2 = 4

so (-4,16) and (2,4) are your answers. You can test these separately and you see that they satisfy both equations when you plug them in.