Question

Okey so I'm suppose to do these equation with substitution and can you guys lakes help me! 6x – 9y = 12 x + y = -18

Answer 1

To solve a system, of equations using the substitution method, you must first solve one equation for one variable.

Answer 2

solve for y in the second equation \(y=-18-x\)
now plug that into the first equation for y

\(6x-9(-18-x)=12\) solve for x

Answer 3

Here are the two equations of the system of equations:

6x – 9y = 12
x + y = -18

Answer 4

Before you even use the substitution method, you can simplify the first equation by dividing both sides by 3 since every coefficient is divisible by 3.
Then the system of equations becomes:
2x – 3y = 4
x + y = -18

Answer 5

Now you need to solve one equation for one variable.
You can pick either equation and either variable, but it's faster if you pick an equation and a variable that are easy to solve for.

Answer 6

Looking at the second equation, you see that the variables x and y don't have coefficients (numbers multiplying them), so pick either x or y and the second equation.

Answer 7

Let's say we choose to solve the second equation for x.
We need to isolate x, so we subtract y from both sides.

2x – 3y = 4 ----(stays the same)----> 2x - 3y = 4
x + y = -18 ----(solved for x)-------> x = -18 - y

Answer 8

Now we do the substitution step.
We take the first equation, and we substitute what x is equal to (from the second equation) into the first equation.

2(-18 - y) - 3y = 4

Now we have one equation with only one variable (y), so we can solve for y.

-36 - 2y - 3y = 4

-36 - 5y = 4

-5y = 40

y = -8

Now we plug in this value of y into either of the original equations and solve for x.
I'll use the second equation because it's easier.

x + y = -18

x + (-8) = -18

x - 8 = -18

x = -10

The solution is: x = -10, y = -8

Answer 9

When you read this, read it a few times and study it. This is how the substitution method works.

Answer 10

If you have any questions, post them. I'll try to answer when I see them.