SOLUTION: Can you please help with 7x+2y=-13 -3x-8y=-23 I am suppose to solve the system by substitution and tell whether it has one no or infinitly solution but I don't understand how do y

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Question 698206: Can you please help with 7x+2y=-13
-3x-8y=-23 I am suppose to solve the system by substitution and tell whether it has one no or infinitly solution but I don't understand how do you solve with all those x and y and how can you tell how many solutins it has
Found 2 solutions by MathLover1, stanbon:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

7x%2B2y=-13
-3x-8y=-23

Solved by pluggable solver: Solving a linear system of equations by subsitution


Lets start with the given system of linear equations

7%2Ax%2B2%2Ay=-13
-3%2Ax-8%2Ay=-23

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

2%2Ay=-13-7%2AxSubtract 7%2Ax from both sides

y=%28-13-7%2Ax%29%2F2 Divide both sides by 2.


Which breaks down and reduces to



y=-13%2F2-%287%2F2%29%2Ax Now we've fully isolated y

Since y equals -13%2F2-%287%2F2%29%2Ax we can substitute the expression -13%2F2-%287%2F2%29%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.


-3%2Ax%2B-8%2Ahighlight%28%28-13%2F2-%287%2F2%29%2Ax%29%29=-23 Replace y with -13%2F2-%287%2F2%29%2Ax. Since this eliminates y, we can now solve for x.

-3%2Ax-8%2A%28-13%2F2%29-8%28-7%2F2%29x=-23 Distribute -8 to -13%2F2-%287%2F2%29%2Ax

-3%2Ax%2B104%2F2%2B%2856%2F2%29%2Ax=-23 Multiply



-3%2Ax%2B52%2B28%2Ax=-23 Reduce any fractions

-3%2Ax%2B28%2Ax=-23-52 Subtract 52 from both sides


-3%2Ax%2B28%2Ax=-75 Combine the terms on the right side



25%2Ax=-75 Now combine the terms on the left side.


cross%28%281%2F25%29%2825%2F1%29%29x=%28-75%2F1%29%281%2F25%29 Multiply both sides by 1%2F25. This will cancel out 25%2F1 and isolate x

So when we multiply -75%2F1 and 1%2F25 (and simplify) we get



x=-3 <---------------------------------One answer

Now that we know that x=-3, lets substitute that in for x to solve for y

-3%28-3%29-8%2Ay=-23 Plug in x=-3 into the 2nd equation

9-8%2Ay=-23 Multiply

-8%2Ay=-23-9Subtract 9 from both sides

-8%2Ay=-32 Combine the terms on the right side

cross%28%281%2F-8%29%28-8%29%29%2Ay=%28-32%2F1%29%281%2F-8%29 Multiply both sides by 1%2F-8. This will cancel out -8 on the left side.

y=-32%2F-8 Multiply the terms on the right side


y=4 Reduce


So this is the other answer


y=4<---------------------------------Other answer


So our solution is

x=-3 and y=4

which can also look like

(-3,4)

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

7%2Ax%2B2%2Ay=-13
-3%2Ax-8%2Ay=-23

we get


graph of 7%2Ax%2B2%2Ay=-13 (red) and -3%2Ax-8%2Ay=-23 (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 (-3,4). This verifies our answer.


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Check:

Plug in (-3,4) into the system of equations


Let x=-3 and y=4. Now plug those values into the equation 7%2Ax%2B2%2Ay=-13

7%2A%28-3%29%2B2%2A%284%29=-13 Plug in x=-3 and y=4


-21%2B8=-13 Multiply


-13=-13 Add


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


So the solution (-3,4) satisfies 7%2Ax%2B2%2Ay=-13



Let x=-3 and y=4. Now plug those values into the equation -3%2Ax-8%2Ay=-23

-3%2A%28-3%29-8%2A%284%29=-23 Plug in x=-3 and y=4


9-32=-23 Multiply


-23=-23 Add


-23=-23 Reduce. Since this equation is true the solution works.


So the solution (-3,4) satisfies -3%2Ax-8%2Ay=-23


Since the solution (-3,4) satisfies the system of equations


7%2Ax%2B2%2Ay=-13
-3%2Ax-8%2Ay=-23


this verifies our answer.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
7x+2y=-13
-3x-8y=-23 I am suppose to solve the system by substitution and tell whether it has one no or infinitly solution
-------------------------
7x+2y=-13
-3x-8y=-23
------
Solve the top equation for "y":
y = (-7x - 13)/2
---------
Substitute for "y" and solve for "x":
-3x - 8(-7x-13)/2 = -23
---------
-3x + (56x+104)/2 = -23
-----
-3x + 28x + 52 = -23
25x = -75
x = -3
-------
Solve for "y":
y = (-7x-13)/2
y = (-7*-3-13)/2
----
y = 4
-------
Ans: one solution
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Cheers,
Stan H.
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