SOLUTION: solve the system of equation by substitution 4x - 6y = 9 5x -6y =1

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Question 89404: solve the system of equation by substitution
4x - 6y = 9
5x -6y =1
Found 2 solutions by jim_thompson5910, checkley75:
Answer by jim_thompson5910(35256) 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

4%2Ax-6%2Ay=9
5%2Ax-6%2Ay=1

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

-6%2Ay=9-4%2AxSubtract 4%2Ax from both sides

y=%289-4%2Ax%29%2F-6 Divide both sides by -6.


Which breaks down and reduces to



y=-3%2F2%2B%282%2F3%29%2Ax Now we've fully isolated y

Since y equals -3%2F2%2B%282%2F3%29%2Ax we can substitute the expression -3%2F2%2B%282%2F3%29%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.


5%2Ax%2B-6%2Ahighlight%28%28-3%2F2%2B%282%2F3%29%2Ax%29%29=1 Replace y with -3%2F2%2B%282%2F3%29%2Ax. Since this eliminates y, we can now solve for x.

5%2Ax-6%2A%28-3%2F2%29-6%282%2F3%29x=1 Distribute -6 to -3%2F2%2B%282%2F3%29%2Ax

5%2Ax%2B18%2F2-%2812%2F3%29%2Ax=1 Multiply



5%2Ax%2B9-4%2Ax=1 Reduce any fractions

5%2Ax-4%2Ax=1-9 Subtract 9 from both sides


5%2Ax-4%2Ax=-8 Combine the terms on the right side



1%2Ax=-8 Now combine the terms on the left side.


cross%28%281%2F1%29%281%2F1%29%29x=%28-8%2F1%29%281%2F1%29 Multiply both sides by 1%2F1. This will cancel out 1%2F1 and isolate x

So when we multiply -8%2F1 and 1%2F1 (and simplify) we get



x=-8 <---------------------------------One answer

Now that we know that x=-8, lets substitute that in for x to solve for y

5%28-8%29-6%2Ay=1 Plug in x=-8 into the 2nd equation

-40-6%2Ay=1 Multiply

-6%2Ay=1%2B40Add 40 to both sides

-6%2Ay=41 Combine the terms on the right side

cross%28%281%2F-6%29%28-6%29%29%2Ay=%2841%2F1%29%281%2F-6%29 Multiply both sides by 1%2F-6. This will cancel out -6 on the left side.

y=41%2F-6 Multiply the terms on the right side


y=-41%2F6 Reduce


So this is the other answer


y=-41%2F6<---------------------------------Other answer


So our solution is

x=-8 and y=-41%2F6

which can also look like

(-8,-41%2F6)

Notice if we graph the equations (if you need help with graphing, check out this solver)

4%2Ax-6%2Ay=9
5%2Ax-6%2Ay=1

we get


graph of 4%2Ax-6%2Ay=9 (red) and 5%2Ax-6%2Ay=1 (green) (hint: you may have to solve for y to graph these) intersecting at the blue circle.


and we can see that the two equations intersect at (-8,-41%2F6). This verifies our answer.


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Check:

Plug in (-8,-41%2F6) into the system of equations


Let x=-8 and y=-41%2F6. Now plug those values into the equation 4%2Ax-6%2Ay=9

4%2A%28-8%29-6%2A%28-41%2F6%29=9 Plug in x=-8 and y=-41%2F6


-32%2B246%2F6=9 Multiply


54%2F6=9 Add


9=9 Reduce. Since this equation is true the solution works.


So the solution (-8,-41%2F6) satisfies 4%2Ax-6%2Ay=9



Let x=-8 and y=-41%2F6. Now plug those values into the equation 5%2Ax-6%2Ay=1

5%2A%28-8%29-6%2A%28-41%2F6%29=1 Plug in x=-8 and y=-41%2F6


-40%2B246%2F6=1 Multiply


6%2F6=1 Add


1=1 Reduce. Since this equation is true the solution works.


So the solution (-8,-41%2F6) satisfies 5%2Ax-6%2Ay=1


Since the solution (-8,-41%2F6) satisfies the system of equations


4%2Ax-6%2Ay=9
5%2Ax-6%2Ay=1


this verifies our answer.

Answer by checkley75(3666) About Me  (Show Source):
You can put this solution on YOUR website!
MULTIPLY EITHER EQUATION BY -1 & ADD.
-4X+6Y=-9
5X-6Y=1
---------------------------------
X=-8 ANSWER. NOW SUBSTITUTE -8 FOR X 7 SOLVE FOR Y
5*-8-6Y=1
-40-6Y=1
-6Y=41
Y=41/-6
Y=-41/6 ANSWER.