7x2 3y2 5 0 3X2 5y2 12Solution7x2 3y2 5 01 3x2 5y2

Solution

7x² - 3y² + 5 = 0...(1)

3x² + 5y² - 12 = 0...(2)

We aere given 2 equations in 2 variables. To solve these, we have to eliminate one of these. Let us multiply the 1st equation by 3 and the 2nd equation by 5. Then we have 21x² - 9y² + 15 = 0...(3) and 21x² + 35 y² - 84 = 0 ...(4) On subtracting the 3rd equation from the 4th equation, we have 21x² + 35y² - 84 - 21x² + 9y² -15 = 0 or, 44y² - 99 = 0 or, y² = 99/44. = 9/4. Therefore y = ± (9/4) = ± 3/2 > On substituting the value of y² = 9/4 in the 2nd equation, we get 3x² + 5 (9/4) - 12 = 0 or, 3x² + 45/4 - 12 = 0 or, 3x² - 3/4 = 0 or x² 1/4. Therefore x = ±1/2. We can verify these values of x and y by substituting in either of the 1st and the 2nd equations.