SOLUTION: -4x+y=-5 2x+y=7

Question 173188This question is from textbook algebra2
: -4x+y=-5
2x+y=7 This question is from textbook algebra2

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

Start with the given system of equations:

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. Notice how the x terms cancel out.

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)

RELATED QUESTIONS
4x-3y=-5... (answered by Maths68)

y=2x +5... (answered by user_dude2008)

y=1/2x-2... (answered by fractalier)

y=4x-1 and y=2x+-5 (answered by Alan3354)

x�-y=4x y-2x=-5 (answered by Math10#)

4x+3y=... (answered by richwmiller)

How do you solve 4x+y=5... (answered by rchill)

linear combination {2x + y=7 {4x... (answered by checkley77)

y=2x+1 y=-4x+7 (answered by josgarithmetic,ikleyn)