# How do solve the following linear system?: # 3x - 2y = -6 , 8x + 3y= -9 #?

##### 2 Answers

#### Explanation:

From (1),

Sub (3) into (2)

Sub (4) into (3)

you can use either elimination or substitution.

the answer is

#### Explanation:

WAY 1) Elimination

Take you two equations and line them up horizontally like so:

Check to see if the x coefficients of the two equations are the same or if the y coefficients are the same. In this case, they are not. So you'll have to multiply both equations by a common factor to either make the y coefficients or the x coefficients be the same. I decided to make the y coefficients the same.

In order to do that, multiply the whole equation by the least common multiple of the y coefficients. So our y coefficients of the two equations are -2 and 3. The LCM of the two numbers is 6. So multiply both the equations by 6.

Notice that now you can add the two equations together to get rid of the y coefficients completely, in other words, you're eliminating it.

+

THIS IS YOUR X VALUE! Now plug in your x value into either of your equations to solve for the y value.

Once simplified, you should get

Your final answer is

WAY 2) Substitution

Solve for a variable in one equation and then substitute that into either the same equation or the other equation given.

STEP 1: For this problem, I decided to solve for x in the equation

STEP 2: Now plug in that what you get as your answer as x into either one of your equations! (you could use

So plug in the x into the equation of your choice:

1)

2)

3)

4)

5)

6)

7)

STEP 3 plug the y value you just found into either one of the equations. I chose the

1)

2)

3)

4)

5)

6)

7)

Your final answer is