SOLUTION: 4x+2y=-6 2x+3y=-3

Question 221568: 4x+2y=-6
2x+3y=-3
Found 2 solutions by drj, jim_thompson5910:
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
4x+2y=-6
2x+3y=-3

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION

Solve:
We'll use substitution. After moving 2*y to the right, we get:
, or . Substitute that
into another equation:
and simplify: So, we know that y=0. Since , x=-1.5.

Answer: .

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

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.

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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