SOLUTION: I'm not sure how to solve the following: Solve the system by substitution. y=6x-11 -2x-3y=-7

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Question 938290: I'm not sure how to solve the following:
Solve the system by substitution.
y=6x-11
-2x-3y=-7
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
y=6x-11
-2x-3y=-7
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-6x%2By=-11
-2x-3y=-7
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Solved by pluggable solver: Solving a linear system of equations by subsitution


Lets start with the given system of linear equations

-6%2Ax%2B1%2Ay=-11
-2%2Ax-3%2Ay=-7

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

1%2Ay=-11%2B6%2AxAdd 6%2Ax to both sides

y=%28-11%2B6%2Ax%29 Divide both sides by 1.


Which breaks down and reduces to



y=-11%2B6%2Ax Now we've fully isolated y

Since y equals -11%2B6%2Ax we can substitute the expression -11%2B6%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.


-2%2Ax%2B-3%2Ahighlight%28%28-11%2B6%2Ax%29%29=-7 Replace y with -11%2B6%2Ax. Since this eliminates y, we can now solve for x.

-2%2Ax-3%2A%28-11%29-3%286%29x=-7 Distribute -3 to -11%2B6%2Ax

-2%2Ax%2B33-18%2Ax=-7 Multiply



-2%2Ax%2B33-18%2Ax=-7 Reduce any fractions

-2%2Ax-18%2Ax=-7-33 Subtract 33 from both sides


-2%2Ax-18%2Ax=-40 Combine the terms on the right side



-20%2Ax=-40 Now combine the terms on the left side.


cross%28%281%2F-20%29%28-20%2F1%29%29x=%28-40%2F1%29%281%2F-20%29 Multiply both sides by 1%2F-20. This will cancel out -20%2F1 and isolate x

So when we multiply -40%2F1 and 1%2F-20 (and simplify) we get



x=2 <---------------------------------One answer

Now that we know that x=2, lets substitute that in for x to solve for y

-2%282%29-3%2Ay=-7 Plug in x=2 into the 2nd equation

-4-3%2Ay=-7 Multiply

-3%2Ay=-7%2B4Add 4 to both sides

-3%2Ay=-3 Combine the terms on the right side

cross%28%281%2F-3%29%28-3%29%29%2Ay=%28-3%2F1%29%281%2F-3%29 Multiply both sides by 1%2F-3. This will cancel out -3 on the left side.

y=-3%2F-3 Multiply the terms on the right side


y=1 Reduce


So this is the other answer


y=1<---------------------------------Other answer


So our solution is

x=2 and y=1

which can also look like

(2,1)

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

-6%2Ax%2B1%2Ay=-11
-2%2Ax-3%2Ay=-7

we get


graph of -6%2Ax%2B1%2Ay=-11 (red) and -2%2Ax-3%2Ay=-7 (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 (2,1). This verifies our answer.


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Check:

Plug in (2,1) into the system of equations


Let x=2 and y=1. Now plug those values into the equation -6%2Ax%2B1%2Ay=-11

-6%2A%282%29%2B1%2A%281%29=-11 Plug in x=2 and y=1


-12%2B1=-11 Multiply


-11=-11 Add


-11=-11 Reduce. Since this equation is true the solution works.


So the solution (2,1) satisfies -6%2Ax%2B1%2Ay=-11



Let x=2 and y=1. Now plug those values into the equation -2%2Ax-3%2Ay=-7

-2%2A%282%29-3%2A%281%29=-7 Plug in x=2 and y=1


-4-3=-7 Multiply


-7=-7 Add


-7=-7 Reduce. Since this equation is true the solution works.


So the solution (2,1) satisfies -2%2Ax-3%2Ay=-7


Since the solution (2,1) satisfies the system of equations


-6%2Ax%2B1%2Ay=-11
-2%2Ax-3%2Ay=-7


this verifies our answer.