Question

Solve the system of equations
-4x+6y=38
x-5y=-20

Answer 1

To solve the system of equations, we can use the substitution method or the elimination method.

Let's solve it using the elimination method:

We can start by multiplying the second equation by 4 to get a -4x term that will cancel out with the -4x term in the first equation.

4(x-5y) = 4(-20) (multiplying both sides by 4)

4x - 20y = -80

Now we have:

-4x + 6y = 38
4x - 20y = -80

Adding the two equations together eliminates the x terms:

-4x + 6y + 4x - 20y = 38 - 80

-14y = -42
Dividing both sides by -14 simplifies the equation:

y = 3

Substituting y = 3 into the second equation:

x - 5(3) = -20

x - 15 = -20
Adding 15 to both sides:

x = -5

So the solution to the system of equations is x = -5 and y = 3.