SOLUTION: Hi! how do you do substitution method for: 9x+5y=-6 4x+3y=2

Question 252213: Hi! how do you do substitution method for: 9x+5y=-6
4x+3y=2
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given system of equations:

Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.

So let's isolate y in the first equation

Start with the first equation

Subtract from both sides

Rearrange the equation

Divide both sides by

Break up the fraction

Reduce

---------------------

Since , we can now replace each in the second equation with to solve for

Plug in into the second equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.

Distribute to

Multiply

Multiply both sides by the LCM of 5. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver)

Distribute and multiply the LCM to each side

Combine like terms on the left side

Add 18 to both sides

Combine like terms on the right side

Divide both sides by -7 to isolate x

Divide

-----------------First Answer------------------------------

So the first part of our answer is:

Since we know that we can plug it into the equation (remember we previously solved for in the first equation).

Start with the equation where was previously isolated.

Plug in

Multiply

Combine like terms and reduce. (note: if you need help with fractions, check out this solver)

-----------------Second Answer------------------------------

So the second part of our answer is:

-----------------Summary------------------------------

So our answers are:

and

which form the point

Now let's graph the two equations (if you need help with graphing, check out this solver)

From the graph, we can see that the two equations intersect at

. This visually verifies our answer.

graph of (red) and (green) and the intersection of the lines (blue circle).

RELATED QUESTIONS
How would you do Subsituion method for 4x=720-3y and... (answered by Fombitz,malaydassharma,solver91311)

4x -12y =5 -x +3y = -1 how do you solve this using the substitution... (answered by MathLover1)

how do you do the substitution... (answered by alaccalac)

Solve by substitution method 2x+y=3 and 4x-3y=5 How do you do this,... (answered by josgarithmetic)

6x+5y=150 9x+10y=270 Explain to me how to do this, using the Substitution... (answered by MathLover1)

how do i solve this system by substitution method. 2x-5y=-1... (answered by ewatrrr)

How do I solve for both methods? directions:Slove the linear equations using both... (answered by Cintchr)

How do you solve 4x+5y=25 and 8x-5y=35 when using substitution (answered by ikleyn)