SOLUTION: Can you solve this for me? Find the values of x and y that solve the following system of equations: -7x-3y+-13 9x-4y=1

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Question 102666: Can you solve this for me?
Find the values of x and y that solve the following system of equations:
-7x-3y+-13

9x-4y=1
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

-7%2Ax-3%2Ay=-13
9%2Ax-4%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

-3%2Ay=-13%2B7%2AxAdd 7%2Ax to both sides

y=%28-13%2B7%2Ax%29%2F-3 Divide both sides by -3.


Which breaks down and reduces to



y=13%2F3-%287%2F3%29%2Ax Now we've fully isolated y

Since y equals 13%2F3-%287%2F3%29%2Ax we can substitute the expression 13%2F3-%287%2F3%29%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.


9%2Ax%2B-4%2Ahighlight%28%2813%2F3-%287%2F3%29%2Ax%29%29=1 Replace y with 13%2F3-%287%2F3%29%2Ax. Since this eliminates y, we can now solve for x.

9%2Ax-4%2A%2813%2F3%29-4%28-7%2F3%29x=1 Distribute -4 to 13%2F3-%287%2F3%29%2Ax

9%2Ax-52%2F3%2B%2828%2F3%29%2Ax=1 Multiply



9%2Ax-52%2F3%2B%2828%2F3%29%2Ax=1 Reduce any fractions

9%2Ax%2B%2828%2F3%29%2Ax=1%2B52%2F3Add 52%2F3 to both sides


9%2Ax%2B%2828%2F3%29%2Ax=3%2F3%2B52%2F3 Make 1 into a fraction with a denominator of 3


9%2Ax%2B%2828%2F3%29%2Ax=55%2F3 Combine the terms on the right side



%2827%2F3%29%2Ax%2B%2828%2F3%29x=55%2F3 Make 9 into a fraction with a denominator of 3

%2855%2F3%29%2Ax=55%2F3 Now combine the terms on the left side.


cross%28%283%2F55%29%2855%2F3%29%29x=%2855%2F3%29%283%2F55%29 Multiply both sides by 3%2F55. This will cancel out 55%2F3 and isolate x

So when we multiply 55%2F3 and 3%2F55 (and simplify) we get



x=1 <---------------------------------One answer

Now that we know that x=1, lets substitute that in for x to solve for y

9%281%29-4%2Ay=1 Plug in x=1 into the 2nd equation

9-4%2Ay=1 Multiply

-4%2Ay=1-9Subtract 9 from both sides

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

cross%28%281%2F-4%29%28-4%29%29%2Ay=%28-8%2F1%29%281%2F-4%29 Multiply both sides by 1%2F-4. This will cancel out -4 on the left side.

y=-8%2F-4 Multiply the terms on the right side


y=2 Reduce


So this is the other answer


y=2<---------------------------------Other answer


So our solution is

x=1 and y=2

which can also look like

(1,2)

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

-7%2Ax-3%2Ay=-13
9%2Ax-4%2Ay=1

we get


graph of -7%2Ax-3%2Ay=-13 (red) and 9%2Ax-4%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 (1,2). This verifies our answer.


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Check:

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


Let x=1 and y=2. Now plug those values into the equation -7%2Ax-3%2Ay=-13

-7%2A%281%29-3%2A%282%29=-13 Plug in x=1 and y=2


-7-6=-13 Multiply


-13=-13 Add


-13=-13 Reduce. Since this equation is true the solution works.


So the solution (1,2) satisfies -7%2Ax-3%2Ay=-13



Let x=1 and y=2. Now plug those values into the equation 9%2Ax-4%2Ay=1

9%2A%281%29-4%2A%282%29=1 Plug in x=1 and y=2


9-8=1 Multiply


1=1 Add


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


So the solution (1,2) satisfies 9%2Ax-4%2Ay=1


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


-7%2Ax-3%2Ay=-13
9%2Ax-4%2Ay=1


this verifies our answer.