Question

Solve simultaneous equations :
x=7-3y
x²-y²= 39​

Answer 1

x = -8 and y = 5 OR x = 6.25 and y = 0.25

Explanation:

x = 7 - 3y (substitute in other equation)

x² - y² = 39

(7 - 3y)² - y² = 39

49 - 42y + 9y² - y² = 39

8y² - 42y + 10 - 0

4y² - 21y + 5 = 0

21 ± √441 - 80 / 8

= 21 ± 19 / 8

y = 40/8 = 5 or 2/8 = 0.25

Case 1: y = 5

x = 7 - 3(5)

= 7 - 15

= -8

Case 2: y = 0.25

x = 7 - 3(0.25)

x = 6.25

Answer 2

(-8,5) and (6.25,0.25)

Explanation:

Crnext77 has already answered this correctly, and with the preferred approach, with an algebraic substitution. Another way to confirm the answer is to graph both equations and find the points they intersect. See the attached image. At a minimum, it helps with understanding how many solutions may be possible, and their approximate values.