Question

Solve the simultaneous equation x + y = 2 and 4y² - x²= 11​

Answer 1

Answer:

The solution sets are ($\frac{1}{3},\frac{5}{3}$) and (5,-3)

Explanation:

We are given two equations and we are supposed to solve these two equations and find their solutions.

x + y = 2

4$y^{2}-x^{2}=11$

Substitute the first equation in the second and make it a quadratic equation in one variable.

4$y^{2}-(2-y)^{2}= 11$

4$y^{2}-(y^{2}-4y+4)=11$

$3y^{2}+4y-4=11$

$3y^{2}+4y-15=$

$3y^{2}+9y-5y-15=0$

(3y-5)(y+3) = 0

y = $\frac{5}{3}$ or y = -3

x = $\frac{1}{3}$ or x = 5

The solution sets are ($\frac{1}{3},\frac{5}{3}$) and (5,-3)