Solve each equation by the substitution method A 2 2 3 2 1 2

Solve each equation by the substitution method.

A. {(2, 2), (3, -2), (-1, 2), (-4, -2)}

B. {(7, 2), (3, -2), (-4, 2), (-3, -1)}

C. {(4, 2), (3, -2), (-5, 2), (-2, -2)}

D. {(3, 2), (3, -2), (-3, 2), (-3, -2)}

x2 - 4y2 = -7 3x2 + y2 = 31

Solution

x^2 - 4y^2 = -7

3x^2 + y^2 = 31

multiply equation 1 with 3 and then calculate eq. 2 minus eq. 1

3x^2 - 12y^2 = -21

3x^2 + y^2 = 31

13y^2 = 52

y^2 = 4

y = +2 or y = -2

A. when y = + 2

x^2 - 4y^2 = -7

x^2 - 4*(2)^2 = -7

x^2 = 9

x = +3 or x = -3

B.

when y = - 2

x^2 - 4y^2 = -7

x^2 - 4*(-2)^2 = -7

x^2 = 9

x = +3 or x = -3

Ans. will be D option.

{(3, 2), (3, -2), (-3, 2), (-3, -2)}