Question

PLEASE PLEASE HELP

question is attached

Answer 1

Short Answer
x1 = 4.8284
x2 = - 0.828
Remark
Substitute the value for y from the first equation into the second equation. Multiply by 4 and then see if it factors out. Solve for x first and then y. 

Step one 
Solve for y in the first equation. Subtract x from both sides.
y = 2 - x

Step Two
Equate the two ys.
2 - x = - 1/4x^2 + 3

Step Three
Bring the left side over to the right side.
0 = -1/4 x^2 + x + 3 -  2 Combine the like terms.
0 = -1/4 x^2 + x + 1      

Step Four
0 = -1/4 x^2 + x + 1      Multiply through by 4
0 = - x^2 + 4x + 4

Step five
This won't factor. The only thing you can do is use the quadratic equation for roots.

a = - 1
b = 4
c = 4

$\text{x = }\dfrac{ -b \pm \sqrt{b^{2} - 4ac} }{2a}$

$\text{x = }\dfrac{ -(4) \pm \sqrt{4^{2} - 4(-1)4}}{-2}$

$\text{x = }\dfrac{ -(4) \pm \sqrt{16 + 16}}{-2}$

$\text{x = } 2 \pm \sqrt{32 }\div -2$

x = 2 +/- sqrt(4^2 * 2) / (- 2)

x = 2 +/- 4 sqrt(2) / - 2
x = 2 -/+ 2 sqrt(2)
x = 2 -/+ 2 *(1.414) 
x = 2 -/+ 2.828

x1 = 4.8284
x2 = - 0.828

Answer 2

Short Answer

x1 = 4.8284

x2 = - 0.828

Remark

Substitute the value for y from the first equation into the second equation. Multiply by 4 and then see if it factors out. Solve for x first and then y. 

Step one 

Solve for y in the first equation. Subtract x from both sides.

y = 2 - x

Step Two

Equate the two ys.

2 - x = - 1/4x^2 + 3

Step Three

Bring the left side over to the right side.

0 = -1/4 x^2 + x + 3 -  2 Combine the like terms.

0 = -1/4 x^2 + x + 1      

Step Four

0 = -1/4 x^2 + x + 1      Multiply through by 4

0 = - x^2 + 4x + 4

Step five

This won't factor. The only thing you can do is use the quadratic equation for roots.

a = - 1

b = 4

c = 4

x = 2 +/- sqrt(4^2 * 2) / (- 2)

x = 2 +/- 4 sqrt(2) / - 2

x = 2 -/+ 2 sqrt(2)

x = 2 -/+ 2 *(1.414) 

x = 2 -/+ 2.828

x1 = 4.8284

I hope this helps

x = 2 +/- sqrt(4^2 * 2) / (- 2)

x = 2 +/- 4 sqrt(2) / - 2

x = 2 -/+ 2 sqrt(2)

x = 2 -/+ 2 *(1.414) 

x = 2 -/+ 2.828

x1 = 4.82