Answer:
- x = -0.90, y = 2.31
- x = 1.40, y = 9.19
Step-by-step explanation:
Equating the expressions for y will give a quadratic in x:
4x^2 +x = 3x +5
4x^2 -2x = 5 . . . . . . collect x-terms on the left
4(x^2 -1/2x) = 5 . . . .factor out the leading coefficient
4(x^2 -1/2x +1/16) = 5 4/16 . . . . complete the square
4(x -1/4)^2 = 84/16 . . . . write the quadratic as a square
x -1/4 = (±√21)/4 . . . . . divide by 4 and take the square root
x = (1 ±√21)/4 . . . . . . . add 1/4
y = 3x +5 = 3(1 ±√21)/4 +5 = (23 ±3√21)/4 . . . . use the linear equation for y
The solutions are ...
x = (1 -√21)/4; y = (23 -3√21)/4 ≈ 2.31
x ≈ -0.89, y ≈ 2.31
x = (1 +√21)/4; y = (23 +3√21)/4
x ≈ 1.40, y ≈ 9.19
