SOLUTION: hi, i need exactly step by step solution using elimination method and check.thank u. 4x+y=1 x-2y=-2

Question 147704This question is from textbook
: hi, i need exactly step by step solution using elimination method and check.thank u.
4x+y=1
x-2y=-2 This question is from textbook

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.

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