SOLUTION: hi, i need to solve this using elimination method and check. 4x+y=1 x-2y=-2

Question 147698This question is from textbook
: hi, i need to solve this using elimination method and check.
4x+y=1
x-2y=-2 This question is from textbook

Found 2 solutions by jim_thompson5910, GKelly:
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 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 y terms cancel out.

Simplify.

Divide both sides by to isolate .

Reduce.

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

Now go back to the first equation.

Plug in .

Multiply.

Remove any zero terms.

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)

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

Check:

Start with the first equation.

Plug in and .

Evaluate and simplify the left side.

Since the equation is true, this means that (0,1) is a solution for the first equation.

Start with the second equation.

Plug in and .

Evaluate and simplify the left side.

Since the equation is true, this means that (0,1) is a solution for the second equation.

Since all of the equations of the system are true, this means that (0,1) is a solution of the system. So this verifies our answer.

Answer by GKelly(4) (Show Source): You can put this solution on YOUR website!
First, multiply the first equation 4x + y = 1 by 2. You'll end up with the following:
2(4x + y =1); 8x + 2y = 2. Now you may eliminate the 2y; see below
8x + 2y = 2
x - 2y = -2
Cancel out the 2y. You will now have 9x = 0 so X = 0
Now, plug 0 into the x value in the first equation so you can then solve for y.
4x + y = 1
4(0) +y = 1
0 + y = 1
y = 1 - 0
y = 1
X = 0 and y = 1
Now plug in these values into the first equation:
4x + y = 1
4(0) + 1 = 1
0 + 1 = 1
1 = 1 YOU'RE DONE.

RELATED QUESTIONS
solve using elimination method and check 4x+y=1... (answered by mangopeeler07)
hi, i need exactly step by step solution using elimination method and check.thank u.... (answered by jim_thompson5910)
hi, i need to solve this using elimination method and check 15x+3y=-12 (answered by jim_thompson5910)
I need all work and steps to this problem please. Solve by elimination method 2y=4x+10 (answered by ankor@dixie-net.com)
hi, i need exact step by ste solution using elimination method and check. 15x+3y=-12 (answered by jim_thompson5910)
solve for x and y for the following equations using elimination method: 0.5x + 2y = 9... (answered by JBarnum)
Helping my daughter and need your help. Need help solving this problem. I need to solve... (answered by Nate)
Solve using addition-subtraction method to solve. and check 4x+6y=16 3x-2y=... (answered by Alan3354)
4x-2y=16 5x+7y=1 We eliminate. y from 1 to get 2y=4x-16 y=2x-8 We then substitute. in... (answered by solver91311)