SOLUTION: 3x-2y=10 x-y=-4 What is the intersecting coordinates? Here is what I figured: 3x-2y=10 -3x -3x -2y/-2=-3x/-2 +10/-2 y= 3/2x-5 x-y=-4 -x -x -y/y= x + 4 Coord

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: 3x-2y=10 x-y=-4 What is the intersecting coordinates? Here is what I figured: 3x-2y=10 -3x -3x -2y/-2=-3x/-2 +10/-2 y= 3/2x-5 x-y=-4 -x -x -y/y= x + 4 Coord      Log On


   

Question 222456: 3x-2y=10
x-y=-4
What is the intersecting coordinates?
Here is what I figured:
3x-2y=10
-3x -3x
-2y/-2=-3x/-2 +10/-2
y= 3/2x-5
x-y=-4
-x -x
-y/y= x + 4
Coordinate is (2,-2)
My teacher marked this wrong
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

3%2Ax-2%2Ay=10
1%2Ax-1%2Ay=-4

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=10-3%2AxSubtract 3%2Ax from both sides

y=%2810-3%2Ax%29%2F-2 Divide both sides by -2.


Which breaks down and reduces to



y=-5%2B%283%2F2%29%2Ax Now we've fully isolated y

Since y equals -5%2B%283%2F2%29%2Ax we can substitute the expression -5%2B%283%2F2%29%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.


1%2Ax%2B-1%2Ahighlight%28%28-5%2B%283%2F2%29%2Ax%29%29=-4 Replace y with -5%2B%283%2F2%29%2Ax. Since this eliminates y, we can now solve for x.

1%2Ax-1%2A%28-5%29-1%283%2F2%29x=-4 Distribute -1 to -5%2B%283%2F2%29%2Ax

1%2Ax%2B5-%283%2F2%29%2Ax=-4 Multiply



1%2Ax%2B5-%283%2F2%29%2Ax=-4 Reduce any fractions

1%2Ax-%283%2F2%29%2Ax=-4-5 Subtract 5 from both sides


1%2Ax-%283%2F2%29%2Ax=-9 Combine the terms on the right side



%282%2F2%29%2Ax-%283%2F2%29x=-9 Make 1 into a fraction with a denominator of 2

%28-1%2F2%29%2Ax=-9 Now combine the terms on the left side.


cross%28%282%2F-1%29%28-1%2F2%29%29x=%28-9%2F1%29%282%2F-1%29 Multiply both sides by 2%2F-1. This will cancel out -1%2F2 and isolate x

So when we multiply -9%2F1 and 2%2F-1 (and simplify) we get



x=18 <---------------------------------One answer

Now that we know that x=18, lets substitute that in for x to solve for y

1%2818%29-1%2Ay=-4 Plug in x=18 into the 2nd equation

18-1%2Ay=-4 Multiply

-1%2Ay=-4-18Subtract 18 from both sides

-1%2Ay=-22 Combine the terms on the right side

cross%28%281%2F-1%29%28-1%29%29%2Ay=%28-22%2F1%29%281%2F-1%29 Multiply both sides by 1%2F-1. This will cancel out -1 on the left side.

y=-22%2F-1 Multiply the terms on the right side


y=22 Reduce


So this is the other answer


y=22<---------------------------------Other answer


So our solution is

x=18 and y=22

which can also look like

(18,22)

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

3%2Ax-2%2Ay=10
1%2Ax-1%2Ay=-4

we get


graph of 3%2Ax-2%2Ay=10 (red) and 1%2Ax-1%2Ay=-4 (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 (18,22). This verifies our answer.


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Check:

Plug in (18,22) into the system of equations


Let x=18 and y=22. Now plug those values into the equation 3%2Ax-2%2Ay=10

3%2A%2818%29-2%2A%2822%29=10 Plug in x=18 and y=22


54-44=10 Multiply


10=10 Add


10=10 Reduce. Since this equation is true the solution works.


So the solution (18,22) satisfies 3%2Ax-2%2Ay=10



Let x=18 and y=22. Now plug those values into the equation 1%2Ax-1%2Ay=-4

1%2A%2818%29-1%2A%2822%29=-4 Plug in x=18 and y=22


18-22=-4 Multiply


-4=-4 Add


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


So the solution (18,22) satisfies 1%2Ax-1%2Ay=-4


Since the solution (18,22) satisfies the system of equations


3%2Ax-2%2Ay=10
1%2Ax-1%2Ay=-4


this verifies our answer.