SOLUTION: i've tried several different ways and can not seem to get this question of elimination, 5y-7x=29 2y+x=4 the x should equal -2 and y should equal 3 i know this because i use

Question 176030: i've tried several different ways and can not seem to get this question of elimination,
5y-7x=29
2y+x=4
the x should equal -2 and y should equal 3
i know this because i used substitution earlier for this question,
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Note: I've rearranged the terms to get the system

Start with the given system of equations:

Multiply the both sides of the second equation by 7.

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 our answer is 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)

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