SOLUTION: Y=3x+11 y=-2x+1 I'm trying to solve this equtation using substitution

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Question 403327: Y=3x+11
y=-2x+1
I'm trying to solve this equtation using substitution
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!

y=3x%2B11
y=-2x%2B1.....write in standard form
-3x+%2B+y+=+11
2x+%2B+y+=+1
Solved by pluggable solver: Solving a linear system of equations by subsitution


Lets start with the given system of linear equations

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

1%2Ay=11%2B3%2AxAdd 3%2Ax to both sides

y=%2811%2B3%2Ax%29 Divide both sides by 1.


Which breaks down and reduces to



y=11%2B3%2Ax Now we've fully isolated y

Since y equals 11%2B3%2Ax we can substitute the expression 11%2B3%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.


2%2Ax%2B1%2Ahighlight%28%2811%2B3%2Ax%29%29=1 Replace y with 11%2B3%2Ax. Since this eliminates y, we can now solve for x.

2%2Ax%2B1%2A%2811%29%2B1%283%29x=1 Distribute 1 to 11%2B3%2Ax

2%2Ax%2B11%2B3%2Ax=1 Multiply



2%2Ax%2B11%2B3%2Ax=1 Reduce any fractions

2%2Ax%2B3%2Ax=1-11 Subtract 11 from both sides


2%2Ax%2B3%2Ax=-10 Combine the terms on the right side



5%2Ax=-10 Now combine the terms on the left side.


cross%28%281%2F5%29%285%2F1%29%29x=%28-10%2F1%29%281%2F5%29 Multiply both sides by 1%2F5. This will cancel out 5%2F1 and isolate x

So when we multiply -10%2F1 and 1%2F5 (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%28-2%29%2B1%2Ay=1 Plug in x=-2 into the 2nd equation

-4%2B1%2Ay=1 Multiply

1%2Ay=1%2B4Add 4 to both sides

1%2Ay=5 Combine the terms on the right side

cross%28%281%2F1%29%281%29%29%2Ay=%285%2F1%29%281%2F1%29 Multiply both sides by 1%2F1. This will cancel out 1 on the left side.

y=5%2F1 Multiply the terms on the right side


y=5 Reduce


So this is the other answer


y=5<---------------------------------Other answer


So our solution is

x=-2 and y=5

which can also look like

(-2,5)

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

-3%2Ax%2B1%2Ay=11
2%2Ax%2B1%2Ay=1

we get


graph of -3%2Ax%2B1%2Ay=11 (red) and 2%2Ax%2B1%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 (-2,5). This verifies our answer.


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Check:

Plug in (-2,5) into the system of equations


Let x=-2 and y=5. Now plug those values into the equation -3%2Ax%2B1%2Ay=11

-3%2A%28-2%29%2B1%2A%285%29=11 Plug in x=-2 and y=5


6%2B5=11 Multiply


11=11 Add


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


So the solution (-2,5) satisfies -3%2Ax%2B1%2Ay=11



Let x=-2 and y=5. Now plug those values into the equation 2%2Ax%2B1%2Ay=1

2%2A%28-2%29%2B1%2A%285%29=1 Plug in x=-2 and y=5


-4%2B5=1 Multiply


1=1 Add


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


So the solution (-2,5) satisfies 2%2Ax%2B1%2Ay=1


Since the solution (-2,5) satisfies the system of equations


-3%2Ax%2B1%2Ay=11
2%2Ax%2B1%2Ay=1


this verifies our answer.