# SOLUTION: Solve each of the following systems by substitution. 8x-4y=16 y=2x-4 4x-12y=5 -x+ 3y=-1

Algebra ->  -> SOLUTION: Solve each of the following systems by substitution. 8x-4y=16 y=2x-4 4x-12y=5 -x+ 3y=-1      Log On

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Question 86048: Solve each of the following systems by substitution.
8x-4y=16
y=2x-4

4x-12y=5
-x+ 3y=-1

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Since y equals we can substitute the expression into y of the 1st 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 -4 to

Multiply

Subtract from both sides

Combine the terms on the right side

Now combine the terms on the left side.
Since this expression is true for any x, we have an identity.

So there are an infinite number solutions. The simple reason is the 2 equations represent 2 lines that overlap each other. So they intersect each other at an infinite number of points.
If we graph and we get
graph of

we can see that these two lines are the same. So this system is dependent

 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 -12. 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 Add to both sides Make -1 into a fraction with a denominator of 4 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