SOLUTION: What is the x-coordinate of the point of intersection for two lines below? X-2y=-2 Y=-6x+40 A, -82\13 B,-42/13 C, 6 D, 7

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Question 701656: What is the x-coordinate of the point of intersection for two lines below?
X-2y=-2
Y=-6x+40
A, -82\13
B,-42/13
C, 6
D, 7
Answer by mouk(232) 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

6%2Ax%2B1%2Ay=40
1%2Ax-2%2Ay=-2

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=40-6%2AxSubtract 6%2Ax from both sides

y=%2840-6%2Ax%29 Divide both sides by 1.


Which breaks down and reduces to



y=40-6%2Ax Now we've fully isolated y

Since y equals 40-6%2Ax we can substitute the expression 40-6%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.


1%2Ax%2B-2%2Ahighlight%28%2840-6%2Ax%29%29=-2 Replace y with 40-6%2Ax. Since this eliminates y, we can now solve for x.

1%2Ax-2%2A%2840%29-2%28-6%29x=-2 Distribute -2 to 40-6%2Ax

1%2Ax-80%2B12%2Ax=-2 Multiply



1%2Ax-80%2B12%2Ax=-2 Reduce any fractions

1%2Ax%2B12%2Ax=-2%2B80Add 80 to both sides


1%2Ax%2B12%2Ax=78 Combine the terms on the right side



13%2Ax=78 Now combine the terms on the left side.


cross%28%281%2F13%29%2813%2F1%29%29x=%2878%2F1%29%281%2F13%29 Multiply both sides by 1%2F13. This will cancel out 13%2F1 and isolate x

So when we multiply 78%2F1 and 1%2F13 (and simplify) we get



x=6 <---------------------------------One answer

Now that we know that x=6, lets substitute that in for x to solve for y

1%286%29-2%2Ay=-2 Plug in x=6 into the 2nd equation

6-2%2Ay=-2 Multiply

-2%2Ay=-2-6Subtract 6 from both sides

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

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

y=-8%2F-2 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=6 and y=4

which can also look like

(6,4)

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

6%2Ax%2B1%2Ay=40
1%2Ax-2%2Ay=-2

we get


graph of 6%2Ax%2B1%2Ay=40 (red) and 1%2Ax-2%2Ay=-2 (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 (6,4). This verifies our answer.


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Check:

Plug in (6,4) into the system of equations


Let x=6 and y=4. Now plug those values into the equation 6%2Ax%2B1%2Ay=40

6%2A%286%29%2B1%2A%284%29=40 Plug in x=6 and y=4


36%2B4=40 Multiply


40=40 Add


40=40 Reduce. Since this equation is true the solution works.


So the solution (6,4) satisfies 6%2Ax%2B1%2Ay=40



Let x=6 and y=4. Now plug those values into the equation 1%2Ax-2%2Ay=-2

1%2A%286%29-2%2A%284%29=-2 Plug in x=6 and y=4


6-8=-2 Multiply


-2=-2 Add


-2=-2 Reduce. Since this equation is true the solution works.


So the solution (6,4) satisfies 1%2Ax-2%2Ay=-2


Since the solution (6,4) satisfies the system of equations


6%2Ax%2B1%2Ay=40
1%2Ax-2%2Ay=-2


this verifies our answer.