SOLUTION: Explain how to apply elimination in solving a system of equations; apply substitution in solving a system of equations. Demonstrate each technique in solving the system 2x + 7y

Question 202943: Explain how to apply elimination in solving a system of equations; apply substitution in solving a system of equations. Demonstrate each technique in solving the system
2x + 7y = 12
5x - 4y = -13
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given system of equations:

Start with the first equation.

Subtract from both sides.

Divide both sides by to isolate .

Rearrange the terms and simplify.

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

Move onto the second equation.

Now plug in .

Distribute.

Multiply both sides by the LCD to clear any fractions.

Distribute and multiply.

Combine like terms on the left side.

Add to both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

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

Since we know that , we can use this to find .

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 .

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)

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