SOLUTION: 2x-4y=40 8x-3y=82 Is there no solution for this problem? I can't come up with anything that works. I need to show work but can't solve it. Thanks

Question 637131: 2x-4y=40
8x-3y=82
Is there no solution for this problem? I can't come up with anything that works. I need to show work but can't solve it. Thanks
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 first equation by 3.

Distribute and multiply.

Multiply the both sides of the second equation by -4.

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)

RELATED QUESTIONS
Need help please: Use substitution to solve system of equations: 2x-y=8 y=2x-3 I... (answered by jim_thompson5910)

8x^2y+3xy-6x-2 divided by 3x^2 I came up with 8y/3+xy-2x-2/3x^2 but the xy part is... (answered by Edwin McCravy)

I need help with solving this system of equation by substitution. 2x-4y=40 8x-3y=82... (answered by josh_jordan)

Hi- I have been working on this problem and I think I am doing it right. I am about... (answered by jim_thompson5910)

-x + y = 4 2x - 5y = -14 I am completely stuck on how to go about doing this... (answered by Fombitz,josmiceli)

I am a math tutor on this site, can someone please help with a method of systems of... (answered by stanbon)

Hello I have a substitution problem with 3 equations, there are no examples in my text... (answered by Earlsdon)

Two contestants run a 440-yard course. The first wins by 4 seconds when given a head... (answered by MathTherapy)

Hi- I teach Adult Basic Education, mostly I help students pass the GED test. I am no... (answered by Fombitz,stanbon)