Question

Solve the following system of equations for x to the nearest hundredth : y + 2x + 1 = 0; 4y - 4x ^ 2 - 12x = - 7

Answer 1

+3.464; -3.464

Explanation:

call A = y + 2x + 1 = 0 => y = (1 - 2x)

call B: 4y - 4(x^2) - 12x = -7

=> replace y from A to B =>

1. 4(1 - 2x) - 4(x^2) - 12x = -7
2. 4 - 8x - 4(x ^ 2) - 12x = -7
3. -8x - 4(x ^ 2) - 12x = -7 - 4 = -11
4. -4(x^2) - (8x - 12x) = -11
5. -4(x^2) + 4x = -11
6. -4(x^2) + 4x + 11 = 0

=> get delta Δ = (-4^2) - 4*(-4 * 11) = 192

=> Δ > 0 => got 2 No

=> x1 =
`(-4 + √(192) )/(2 * -4)` =
`(1 - 2√(3) )/(2)` = -1.232

=> x2 =
`(-4 - √(192) )/(2 * -4)`=
`(1 + 2√(3) )/(2)`= 2.232

=> replace x from B into A

=> y1 = (1 - 2x) = (1 - 2 * -1.232) = 3.464

=> y2 = (1 - 2x) = (1 - 2 * 2.232) = - 3.464