Question

Create a system of equations with a solution of (5,-2)​

Answer 1

5x - y = 27 and 2x + y = 8 are the system of equations with a solution of (5,-2)​

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

Verify:

Solve eqn 1 and eqn 2

Add both eqn 1 and eqn 2

7x = 35

x = 5

Substitute x = 5 in eqn 2

2(5) + y = 8

y = 8 - 10

y = -2

Thus solution is (5, -2) and the found system of equations are correct