SOLUTION: Could someone tell me if I got these problems right? The first two are the Substitution Method, and the second two are using the Elimination Method. 1) x + y = 15 4x + 3y

Question 145383: Could someone tell me if I got these problems right? The first two are the Substitution Method, and the second two are using the Elimination Method.
1) x + y = 15
4x + 3y = 38
2)-3x + y = -4
x - y = 0

The Elimination Method:
1) 5x - y = 12
3x + y = 4

2) 2x - y = -6
2x - 2y = -4
Thank you in advance. Elle J
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Well it's hard to tell what you got if you don't post your solutions =)

I'll do one of each to help you in the right direction.

# 1
Jump to problem #3

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 first 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

Combine like terms on the left side

Subtract 45 from both sides

Combine like terms on the right side

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

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

So the second part of our answer is:

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

So our answers are:

and

which form the point

# 3
Jump to problem #1

Start with the given system of equations:

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

In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for , we would have to eliminate (or vice versa).

So lets eliminate . In order to do that, we need to have both coefficients that are equal in magnitude but have opposite signs (for instance 2 and -2 are equal in magnitude but have opposite signs). This way they will add to zero. By adding to zero, they can be eliminated.

So to make the coefficients equal in magnitude but opposite in sign, we need to multiply both coefficients by some number to get them to an common number. So if we wanted to get and to some equal number, we could try to get them to the LCM.

Since the LCM of and is , we need to multiply both sides of the top equation by and multiply both sides of the bottom equation by like this:

Multiply the top equation (both sides) by
Multiply the bottom equation (both sides) by

Distribute and multiply

Now add the equations together. In order to add 2 equations, group like terms and combine them

Combine like terms and simplify

Notice how the x terms cancel out

Simplify

Divide both sides by to isolate y

Reduce

Now plug this answer into the top equation to solve for x

Start with the first equation

Plug in

Multiply

Subtract 2 from both sides

Combine like terms on the right side

Divide both sides by 5 to isolate x

Divide

So our answer is
and

which also looks like

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).

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