Solution:
Given that,
create a system of equations with a solution of (5,-2)
The equation for a line in slope intercept form:
y = mx + b
Where, m is the slope and b is the y intercept
For (x, y) = (5, -2)
-2 = 5m + b
When m = 5
-2 = 5(5) + b
-2 = 25 + b
b = -2 - 25
b = -27
When m = -2
-2 = 5(-2) + b
-2 = -10 + b
b = 8
Thus equations are:
y = 5x - 27
y = -2x + 8
Rearranging to standard form,
5x - y = 27 --- eqn 1
2x + y = 8 ---- eqn 2
Thus the system of equations are found
Solve eqn 1 and eqn 2
Add both eqn 1 and eqn 2
7x = 35
Substitute x = 5 in eqn 2
2(5) + y = 8
y = 8 - 10
Thus solution is (5, -2) and the found system of equations are correct
