Question

Find a solution to this system of equations:

5x-3y=20
15x+6y=60

Write your solution in (x,y) form.

Please help!!!!!

Answer 1

(x, y) = (4, 0)

Explanation:

You want the solution to the system of equations ...

• 5x -3y = 20
• 15x +6y = 60

Standard form

It often works well to start the solution process by putting both equations into standard form. We do that by removing any common factors from the coefficients. Here, we see that the second equation's coefficients each have a factor of 3, so we can remove that and rewrite the system as ...

• 5x -3y = 20
• 5x +2y = 20

Observation

Changing the coefficient of the y-term has no effect, telling us that y=0, and the equation reduces to ...

5x = 20

x = 4

More formally, if we subtract the first equation from the second, we get ...

(5x +2y) -(5x -3y) = (20) -(20)

5y = 0 . . . . . . simplify

y = 0 . . . . . . . divide by 5

The solution is (x, y) = (4, 0).