SOLUTION: Use substitution to solve the system. (Simplify your answer completely. If there is no solution, enter NO SOLUTION.) 3y = −12x + 8 4x + y = 3

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Question 1130673: Use substitution to solve the system. (Simplify your answer completely. If there is no solution, enter NO SOLUTION.)
3y = −12x + 8
4x + y = 3
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!



in standard form:



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 3.


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 1 to

Multiply



Reduce any fractions

Subtract from both sides


Make 3 into a fraction with a denominator of 3


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
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Use substitution to solve the system. (Simplify your answer completely. If there is no solution, enter NO SOLUTION.)
3y = −12x + 8
4x + y = 3
3y = - 12x + 8 ------ eq (i)

4x + y = 3_______y = 3 - 4x ------ eq (ii)

From eq (ii), SIMPLY substitute 3 - 4x in eq (i) for y to get:

3(3 - 4x) = - 12x + 8

9 - 12x = - 12x + 8

- 12x + 12x = 8 - 9

From above, we see that: .

Therefore, the system has NO SOLUTIONS, and both graphs will be PARALLEL, as they have the same SLOPE.

That's it! NOTHING more, NOTHING less! 

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