SOLUTION: Think i did them right but 2 & 3 are I get no solution and want to make sure I am not leaving something out. 1. Solve by substitution or elimination method: 3x

Question 185456: Think i did them right but 2 & 3 are I get no solution and want to make sure I am not leaving something out.
1. Solve by substitution or elimination method:
3x � 2y = 26
-7x + 3y = -49
2. Solve by substitution or elimination method:
4x � 5y = 14
-12x + 15y = -42
3. Solve by substitution or elimination method:
-2x + 6y = 19
10x � 30y = -15

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
# 1

Let's solve this system by elimination

Start with the given system of equations:

Multiply the both sides of the first equation by 3.

Distribute and multiply.

Multiply the both sides of the second equation by 2.

Distribute and multiply.

So we have the new system of equations:

Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:

Group like terms.

Combine like terms.

Simplify.

Divide both sides by to isolate .

Reduce.

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

Now go back to the first equation.

Plug in .

Multiply.

Subtract from both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

So the solutions are and .

Which form the ordered pair

.

This means that the system is consistent and independent.

Notice when we graph the equations, we see that they intersect at

. So this visually verifies our answer.

Graph of (red) and (green)

================================================================

# 2

Let's solve this system by elimination

Start with the given system of equations:

Multiply the both sides of the first equation by 3.

Distribute and multiply.

So we have the new system of equations:

Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:

Group like terms.

Combine like terms.

Simplify.

Since is always true, this means that there are an infinite number of solutions.

So the system is consistent and dependent.

================================================================

# 3

Start with the given system of equations:

Multiply the both sides of the first equation by 5.

Distribute and multiply.

So we have the new system of equations:

Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:

Group like terms.

Combine like terms.

Simplify.

Since is never true, this means that there are no solutions.

So the system is inconsistent.

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