SOLUTION: Actually, I'm not sure what section this is in, but I really need help! Please, if you could help me, I need to solve the following equation: 4x+6y=3 2x+3y=-2

Question 117242: Actually, I'm not sure what section this is in, but I really need help! Please, if you could help me, I need to solve the following equation:
4x+6y=3
2x+3y=-2
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Solved by pluggable solver: Solving a linear system of equations by subsitution

Lets start with the given system of linear equations

Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to choose y.

Solve for y for the first equation

Subtract from both sides

Divide both sides by 6.

Which breaks down and reduces to

Now we've fully isolated y

Since y equals we can substitute the expression into y of the 2nd equation. This will eliminate y so we can solve for x.

Replace y with . Since this eliminates y, we can now solve for x.

Distribute 3 to

Multiply

Reduce any fractions

Subtract from both sides

Make -2 into a fraction with a denominator of 2

Combine the terms on the right side

Now combine the terms on the left side.
Since this expression is not true, we have an inconsistency.

So there are no solutions. The simple reason is the 2 equations represent 2 parallel lines that will never intersect. Since no intersections occur, no solutions exist.

graph of (red) and (green) (hint: you may have to solve for y to graph these)

and we can see that the two equations are parallel and will never intersect. So this system is inconsistent

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