SOLUTION: Solve the system of equations below by the substitution method. -5x+8y=-18 -10x+16y=-14 a.(-11/10,-11/16) b.(-11/16,-11/10) c.(11/16,11/10) d.no solution e.(-5/2,25/16)

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Solve the system of equations below by the substitution method. -5x+8y=-18 -10x+16y=-14 a.(-11/10,-11/16) b.(-11/16,-11/10) c.(11/16,11/10) d.no solution e.(-5/2,25/16)       Log On


   

Question 472588: Solve the system of equations below by the substitution method.
-5x+8y=-18
-10x+16y=-14
a.(-11/10,-11/16)
b.(-11/16,-11/10)
c.(11/16,11/10)
d.no solution
e.(-5/2,25/16)


Answer by MathLover1(20850) About Me  (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

-5%2Ax%2B8%2Ay=-18
-10%2Ax%2B16%2Ay=-14

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

8%2Ay=-18%2B5%2AxAdd 5%2Ax to both sides

y=%28-18%2B5%2Ax%29%2F8 Divide both sides by 8.


Which breaks down and reduces to



y=-9%2F4%2B%285%2F8%29%2Ax Now we've fully isolated y

Since y equals -9%2F4%2B%285%2F8%29%2Ax we can substitute the expression -9%2F4%2B%285%2F8%29%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.


-10%2Ax%2B16%2Ahighlight%28%28-9%2F4%2B%285%2F8%29%2Ax%29%29=-14 Replace y with -9%2F4%2B%285%2F8%29%2Ax. Since this eliminates y, we can now solve for x.

-10%2Ax%2B16%2A%28-9%2F4%29%2B16%285%2F8%29x=-14 Distribute 16 to -9%2F4%2B%285%2F8%29%2Ax

-10%2Ax-144%2F4%2B%2880%2F8%29%2Ax=-14 Multiply



-10%2Ax-36%2B10%2Ax=-14 Reduce any fractions

-10%2Ax%2B10%2Ax=-14%2B36Add 36 to both sides


-10%2Ax%2B10%2Ax=22 Combine the terms on the right side



0%2Ax=22 Now combine the terms on the left side.
0%2F1=22%2F1 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 -5%2Ax%2B8%2Ay=-18 (red) and -10%2Ax%2B16%2Ay=-14 (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


so the answer is:
d.no solution