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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
x2 = - 0.828
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
x2 = - 0.828