Answer:
(4, - 7 ) is the only solution to the system of equations
Explanation:
to determine if a point is a solution to the system of equations
substitute the coordinates of each point into the equations and check for validity.
Note that for a point to be a solution it must satisfy BOTH equations
y = - 4x + 9
7x + 5y = - 7
(2, 1 )
y = - 4(2) + 9 = - 8 + 9 = 1 ← True
7(2) + 5(1) = 14 + 5 = 19 ≠ 1 ← False
Only 1 equation is satisfied
(2, 1 ) is NOT a solution
(- 6, - 3 )
y = - 4(- 6) + 9 = 24 + 9 = 33 ≠ - 3 ← False
7(- 6) + 5(- 3) = - 42 - 15 = - 57 ≠ - 3 ← False
Neither of the 2 equations are satisfied
(- 6, - 3 ) is NOT a solution
(4, - 7 )
y = - 4(4) + 9 = - 16 + 9 = - 7 ← True
7(4) + 5(- 7) = 28 - 35 = - 7 ← True
Both equations are satisfied
(4, - 7 ) is a Solution
(- 1, 0 )
y = - 4(- 1) + 9 = 4 + 9 = 13 ≠ 0 ← False
7(- 1) + 5(0) = - 7 + 0 = - 7 ← True
Only 1 equation is satisfied
(- 1, 0 ) is NOT a solution