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

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!

3y+=+-12x+%2B+8
4x+%2B+y+=+3
in standard form:
12x%2B3y+=+8
4x+%2B+y+=+3

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


Lets start with the given system of linear equations

12%2Ax%2B3%2Ay=8
4%2Ax%2B1%2Ay=3

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

3%2Ay=8-12%2AxSubtract 12%2Ax from both sides

y=%288-12%2Ax%29%2F3 Divide both sides by 3.


Which breaks down and reduces to



y=8%2F3-4%2Ax Now we've fully isolated y

Since y equals 8%2F3-4%2Ax we can substitute the expression 8%2F3-4%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.


4%2Ax%2B1%2Ahighlight%28%288%2F3-4%2Ax%29%29=3 Replace y with 8%2F3-4%2Ax. Since this eliminates y, we can now solve for x.

4%2Ax%2B1%2A%288%2F3%29%2B1%28-4%29x=3 Distribute 1 to 8%2F3-4%2Ax

4%2Ax%2B8%2F3-4%2Ax=3 Multiply



4%2Ax%2B8%2F3-4%2Ax=3 Reduce any fractions

4%2Ax-4%2Ax=3-8%2F3 Subtract 8%2F3 from both sides


4%2Ax-4%2Ax=9%2F3-8%2F3 Make 3 into a fraction with a denominator of 3


4%2Ax-4%2Ax=1%2F3 Combine the terms on the right side



0%2Ax=1%2F3 Now combine the terms on the left side.
0%2F1=1%2F3 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%28+500%2C+600%2C+-6%2C+5%2C+-10%2C+10%2C+%288-12%2Ax%29%2F3%2C+%283-4%2Ax%29%2F1+%29+ graph of 12%2Ax%2B3%2Ay=8 (red) and 4%2Ax%2B1%2Ay=3 (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) About Me  (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: highlight_green%280+%3C%3E+-+1%29.

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!