Question

Solve the system using elimination.
3x – 9y = 18
x + 2y = 1

Answer 1

To use the elimination method, you must first solve one equation for one variable.

Look at the second equation. Since one term in it is just x, solve the second equation for x by subtracting 2y from both sides. What do you get?

Answer 2

You actually solved the first equation for x. That was not what I asked, but it was correct.

Answer 3

x=1−2y SECOND equation, sorry.

Answer 4

Great.
Now that we have one equation solved for one variable, we do the "substitution" step. that's why this method is called the substitution method.

Answer 5

Take what x is equal to form the second equation, you know x equals 1 - 2y, and substitute x in the first equation by 1 - 2y.

Answer 6

\(3\color{red}{x} - 9y = 18\)

\( x = \color{red}{1 - 2y}\)

Substitute the x in red of the first equation by the red expression of the second equation. You'll need parentheses around the expresssion.

Answer 7

then what?

Answer 8

Look at the first equation just above.
You see the red x?

Answer 9

Substitute the red x with 1 - 2y from the other equation.

You get:

\(3 \color{red}{(1 - 2y) } - 9y = 18\)

Now distribute the 3:

\(3 - 6y - 9y = 18\)

Combine like terms:

3 - 15y = 18\)

Subtract 15 from both sides:

-15y = 15

Divide both sides by -15:

y = -1

Answer 10

Now that we know that y = -1, we substitute that value into y of either one of the original equations.

Let's use the second original equation:

x + 2y = 1

x + 2(-1) = 1

x - 2 = 1

x = 3

The solution is x = 3 and y = -1