What is 4x^2-9y^2=12,2x-3y=2 ?

The solution to 4x^2-9y^2=12,2x-3y=2 is

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4x^2-9y^2=12,2x-3y=2

4 x^{2} - 9 y^{2} = 12, 2 x - 3 y = 2

(x = 2, y = \frac{2}{3})

Solution steps

[4 x^{2} - 9 y^{2} = 12 2 x - 3 y = 2]

Isolate

x

for

2 x - 3 y = 2 : x = \frac{2 + 3 y}{2}

Plug the solutions

x = \frac{2 + 3 y}{2}

into

4 x^{2} - 9 y^{2} = 12

For

4 x^{2} - 9 y^{2} = 12

, subsitute

x

with

\frac{2 + 3 y}{2} : y = \frac{2}{3}

Plug the solutions

y = \frac{2}{3}

into

2 x - 3 y = 2

For

2 x - 3 y = 2

, subsitute

y

with

\frac{2}{3} : x = 2

Verify solutions by plugging them into the original equations

Therefore, the final solution for

4 x^{2} - 9 y^{2} = 12, 2 x - 3 y = 2

(x = 2, y = \frac{2}{3})

9 y^{2} - 45 y + 56 = 4, x^{2} - 17 y + 18 = 0

x^{2} + 3 y^{2} = 12, x - y = 2

4 a + b = 6, 4 a + b = 1

b = 4 a, c = 5

x + 2 y = 8, - x - 2 y = - 8