Question

Solve the pair of equation 2x – y=9 4x^2 + 3y^2– 2x + y = 16​

Answer 1

Answer:

$x=\frac{27+\sqrt143i}{8}{} ,\frac{27-\sqrt{143i} }{8}$

$y=-9+\frac{27+\sqrt{143} i}{4} ,-9+\frac{27-\sqrt{143} i}{4}$

Step-by-step explanation:

1) Solve for 2x - y = 9

A. Solve for y.

2x - y = 9

B. Subtract 2x from both sides.

-y = 9 - 2x

C. Multiply both sides by -1.

y = -9 + 2x

D. Regroup terms.

y = 2x - 9

2) Substitute y = 2x- 9 into 4x² + 3y² - 2x + y = 16

A. Start with the original equation.

4x² + 3y² - 2x + y = 16

B. Let y = 2x - 9.

4x² + 3(2x - 9)² - 2x + 2x - 9 = 16

C. Simplify.

16x² - 108x + 234 = 16

3) Solve for x in 16x² - 108x + 234 = 16

A. Solve for x.

16x² - 108x + 234 -= 16

B. Move all terms to one side.

16x² - 108x + 234 - 16 = 0

C. Simplify 16x² - 108x + 234 - 16 to 16 x² - 108x + 218

16 x² - 108x + 218 = 0

D. Use the Quadratic Formula.

$x=\frac{108+4\sqrt{143}i }{32}$, $\frac{108-4\sqrt{143} i}{32}$

E. Simplify solutions.

$x=\frac{27+\sqrt{143} i}{8} ,\frac{27-\sqrt{143} i}{8}$

4) Substitute $x=\frac{27+\sqrt{143}i }{8} ,\frac{27-\sqrt{143}i }{8}$ into y = 2x - 9.

1) Start with the original equation.

y = 2x - 9

2) Let x = $\frac{27+\sqrt{143} i}{8} ,\frac{27-\sqrt{143}i }{8} .$

$y=2*\frac{27+\sqrt{143} i}{8} -9,2*\frac{27-\sqrt{143}i }{8} -9$

3) Simplify

$y=-9+\frac{27+\sqrt{143}i }{4} ,-9+\frac{27-\sqrt{143i} }{4}$