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

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

4x-12y=5
-x+ 3y=-1
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Lets start with the given system of linear equations

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

RELATED QUESTIONS
Solve each of the following systems by substitution. 5x - 2y= -5 y - 5x = 3 8x (answered by checkley75)

Solve each of the following systems by substitution. 16. 5x -2y = -5 y-5x = 3 (answered by checkley71)

QUESTION: SOLVE EACH OF THE FOLLOWING SYSTEMS BY SUBSTITUION 20. 8X-4Y=16 I BELIVE (answered by stanbon)

Solve each of the following systems by substitution. 4x � 12y = 5 -x + 3y =... (answered by fractalier)

Solve each of the following systems by substitution 4x - 12y = 5 -x + 3y = -1 (answered by jim_thompson5910)

Solve each of the following systems by substitution 4x - 12y = 5 -x + 3y = -1 (answered by checkley75)

solve each of the following systems by substitution: 4x-12y=5... (answered by Earlsdon)

Solve each of the following systems by substitution. 4x-12y=5... (answered by jim_thompson5910)