Question

Solve the following system of equations.
6x+5y=-10
3x+5y=20

Answer 1

You sure?

Answer 2

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

First, we will isolate one of the variables in one of the equations. Let's isolate y in the first equation:

6x + 5y = -10
5y = -10 - 6x
y = (-10 - 6x) / 5
y = -2 - 6/5x

Now we can substitute this expression for y into the second equation:

3x + 5(-2 - 6/5x) = 20
3x - 10 - 6x = 20
-3x - 10 = 20
-3x = 30
x = -10

Now that we have found the value of x, we can substitute it back into either of the original equations to solve for y. Let's use the first equation:

6(-10) + 5y = -10
-60 + 5y = -10
5y = 50
y = 10

So the solution to the system of equations is x = -10 and y = 10.

Answer 3

Let's check the solution by substituting x = -10 and y = 10 back into both equations:

For the first equation:
6x + 5y = -10
6(-10) + 5(10) = -10
-60 + 50 = -10
-10 = -10

The first equation holds true.

For the second equation:
3x + 5y = 20
3(-10) + 5(10) = 20
-30 + 50 = 20
20 = 20

The second equation also holds true.

Therefore, the solution x = -10 and y = 10 is correct.