SOLUTION: what multiplier should be used for each of the following equations to eliminate one unknown by subtraction? 3x-y=7 2x+7y=42

Question 252508: what multiplier should be used for each of the following equations to eliminate one unknown by subtraction?
3x-y=7
2x+7y=42
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
The multiplier is 7 since this will change -y into -7y. Add this to 7y to get -7+7y=0y=0 which means that it cancels out.

Start with the given system of equations:

Multiply the both sides of the first equation by 7.

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 .

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

Now go back to the first equation.

Plug in .

Multiply.

Multiply both sides by the LCD to clear any fractions.

Distribute and 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.

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