SOLUTION: -8x � 4y = -68 x + 3y = 16

Question 550713: -8x � 4y = -68
x + 3y = 16
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 8.

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.

Add to 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)

RELATED QUESTIONS
Solve using the substitution method. Show your work. If the system has no solution or an (answered by mananth)

Solve using the substitution method. Show your work. If the system has no solution or an... (answered by ewatrrr)

solve using the sustition method show work if system has no solution or an infinite... (answered by stanbon)

Solve using the substitution method. Show your work. If the system has no solution or an... (answered by unlockmath)

[ -x + 3y = -9 ] [ 8x-4y = 32... (answered by TimothyLamb)

Simplify: -3y -5x -8x -4y... (answered by t0hierry)

Solve each of the following systems by substitution. 8x-4y=16 y=2x-4 4x-12y=5... (answered by jim_thompson5910)

8x+4y=16 (answered by Alan3354)

4y-8x=-16 (answered by farohw)