SOLUTION: This question confused me. 2(x+1)-(y-4)=15 3(x-1)+4(y+2)=2

Question 174867: This question confused me.
2(x+1)-(y-4)=15
3(x-1)+4(y+2)=2
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the first equation.

Distribute

Combine like terms.

Subtract 6 from both sides.

Combine like terms.

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

Move onto the second equation.

Distribute

Combine like terms.

Subtract 5 from both sides.

Combine like terms.

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

So we have the system of equations:

Let's solve this system by substitution

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

Combine like terms on the left side

Add 36 to both sides

Combine like terms on the right side

Divide both sides by 11 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

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

So the second part of our answer is:

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

So our answers are:

and

which form the ordered pair

This means that the system is consistent and independent.

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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