SOLUTION: 2x- y = -4 -3x + y = -9

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Question 119604This question is from textbook glenco mathmatics
: 2x- y = -4
-3x + y = -9 This question is from textbook glenco mathmatics

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

2%2Ax-1%2Ay=-4
-3%2Ax%2B1%2Ay=-9

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=-4-2%2AxSubtract 2%2Ax from both sides

y=%28-4-2%2Ax%29%2F-1 Divide both sides by -1.


Which breaks down and reduces to



y=4%2B2%2Ax Now we've fully isolated y

Since y equals 4%2B2%2Ax we can substitute the expression 4%2B2%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.


-3%2Ax%2B1%2Ahighlight%28%284%2B2%2Ax%29%29=-9 Replace y with 4%2B2%2Ax. Since this eliminates y, we can now solve for x.

-3%2Ax%2B1%2A%284%29%2B1%282%29x=-9 Distribute 1 to 4%2B2%2Ax

-3%2Ax%2B4%2B2%2Ax=-9 Multiply



-3%2Ax%2B4%2B2%2Ax=-9 Reduce any fractions

-3%2Ax%2B2%2Ax=-9-4 Subtract 4 from both sides


-3%2Ax%2B2%2Ax=-13 Combine the terms on the right side



-1%2Ax=-13 Now combine the terms on the left side.


cross%28%281%2F-1%29%28-1%2F1%29%29x=%28-13%2F1%29%281%2F-1%29 Multiply both sides by 1%2F-1. This will cancel out -1%2F1 and isolate x

So when we multiply -13%2F1 and 1%2F-1 (and simplify) we get



x=13 <---------------------------------One answer

Now that we know that x=13, lets substitute that in for x to solve for y

-3%2813%29%2B1%2Ay=-9 Plug in x=13 into the 2nd equation

-39%2B1%2Ay=-9 Multiply

1%2Ay=-9%2B39Add 39 to both sides

1%2Ay=30 Combine the terms on the right side

cross%28%281%2F1%29%281%29%29%2Ay=%2830%2F1%29%281%2F1%29 Multiply both sides by 1%2F1. This will cancel out 1 on the left side.

y=30%2F1 Multiply the terms on the right side


y=30 Reduce


So this is the other answer


y=30<---------------------------------Other answer


So our solution is

x=13 and y=30

which can also look like

(13,30)

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

2%2Ax-1%2Ay=-4
-3%2Ax%2B1%2Ay=-9

we get


graph of 2%2Ax-1%2Ay=-4 (red) and -3%2Ax%2B1%2Ay=-9 (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 (13,30). This verifies our answer.


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Check:

Plug in (13,30) into the system of equations


Let x=13 and y=30. Now plug those values into the equation 2%2Ax-1%2Ay=-4

2%2A%2813%29-1%2A%2830%29=-4 Plug in x=13 and y=30


26-30=-4 Multiply


-4=-4 Add


-4=-4 Reduce. Since this equation is true the solution works.


So the solution (13,30) satisfies 2%2Ax-1%2Ay=-4



Let x=13 and y=30. Now plug those values into the equation -3%2Ax%2B1%2Ay=-9

-3%2A%2813%29%2B1%2A%2830%29=-9 Plug in x=13 and y=30


-39%2B30=-9 Multiply


-9=-9 Add


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


So the solution (13,30) satisfies -3%2Ax%2B1%2Ay=-9


Since the solution (13,30) satisfies the system of equations


2%2Ax-1%2Ay=-4
-3%2Ax%2B1%2Ay=-9


this verifies our answer.