SOLUTION: this is part of my summer math work and i dont know how to solve it ... {{{6x - 18y = 60}}} {{{9x + 2y = 32 }}} i tried to use the solver on here but it doesnt explain HOW to

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: this is part of my summer math work and i dont know how to solve it ... {{{6x - 18y = 60}}} {{{9x + 2y = 32 }}} i tried to use the solver on here but it doesnt explain HOW to       Log On


   

Question 91934: this is part of my summer math work and i dont know how to solve it ...
6x+-+18y+=+60
9x+%2B+2y+=+32+
i tried to use the solver on here but it doesnt explain HOW to get the answer.
Found 2 solutions by homeworkhelpanytime, jim_thompson5910:
Answer by homeworkhelpanytime(21) About Me  (Show Source):
You can put this solution on YOUR website!
6x - 18y = 60 ......(1)
9x + 2y = 32 ......(2)
multiply equation (2) by 9 we get
81x + 18y = 288
adding equation (1) and (3)
6x - 18y + 81x + 18y = 60 + 288
87x = 348
x = 4
putting the value of x =4 in equation (1)
6*4 - 18y = 60
y = 2












Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If you're looking for a substitution solver, then check out this solver (it will show you how to get the solution step-by-step)


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


Lets start with the given system of linear equations

6%2Ax-18%2Ay=60
9%2Ax%2B2%2Ay=32

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

-18%2Ay=60-6%2AxSubtract 6%2Ax from both sides

y=%2860-6%2Ax%29%2F-18 Divide both sides by -18.


Which breaks down and reduces to



y=-10%2F3%2B%281%2F3%29%2Ax Now we've fully isolated y

Since y equals -10%2F3%2B%281%2F3%29%2Ax we can substitute the expression -10%2F3%2B%281%2F3%29%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.


9%2Ax%2B2%2Ahighlight%28%28-10%2F3%2B%281%2F3%29%2Ax%29%29=32 Replace y with -10%2F3%2B%281%2F3%29%2Ax. Since this eliminates y, we can now solve for x.

9%2Ax%2B2%2A%28-10%2F3%29%2B2%281%2F3%29x=32 Distribute 2 to -10%2F3%2B%281%2F3%29%2Ax

9%2Ax-20%2F3%2B%282%2F3%29%2Ax=32 Multiply



9%2Ax-20%2F3%2B%282%2F3%29%2Ax=32 Reduce any fractions

9%2Ax%2B%282%2F3%29%2Ax=32%2B20%2F3Add 20%2F3 to both sides


9%2Ax%2B%282%2F3%29%2Ax=96%2F3%2B20%2F3 Make 32 into a fraction with a denominator of 3


9%2Ax%2B%282%2F3%29%2Ax=116%2F3 Combine the terms on the right side



%2827%2F3%29%2Ax%2B%282%2F3%29x=116%2F3 Make 9 into a fraction with a denominator of 3

%2829%2F3%29%2Ax=116%2F3 Now combine the terms on the left side.


cross%28%283%2F29%29%2829%2F3%29%29x=%28116%2F3%29%283%2F29%29 Multiply both sides by 3%2F29. This will cancel out 29%2F3 and isolate x

So when we multiply 116%2F3 and 3%2F29 (and simplify) we get



x=4 <---------------------------------One answer

Now that we know that x=4, lets substitute that in for x to solve for y

9%284%29%2B2%2Ay=32 Plug in x=4 into the 2nd equation

36%2B2%2Ay=32 Multiply

2%2Ay=32-36Subtract 36 from both sides

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

cross%28%281%2F2%29%282%29%29%2Ay=%28-4%2F1%29%281%2F2%29 Multiply both sides by 1%2F2. This will cancel out 2 on the left side.

y=-4%2F2 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=4 and y=-2

which can also look like

(4,-2)

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

6%2Ax-18%2Ay=60
9%2Ax%2B2%2Ay=32

we get


graph of 6%2Ax-18%2Ay=60 (red) and 9%2Ax%2B2%2Ay=32 (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 (4,-2). This verifies our answer.


-----------------------------------------------------------------------------------------------
Check:

Plug in (4,-2) into the system of equations


Let x=4 and y=-2. Now plug those values into the equation 6%2Ax-18%2Ay=60

6%2A%284%29-18%2A%28-2%29=60 Plug in x=4 and y=-2


24%2B36=60 Multiply


60=60 Add


60=60 Reduce. Since this equation is true the solution works.


So the solution (4,-2) satisfies 6%2Ax-18%2Ay=60



Let x=4 and y=-2. Now plug those values into the equation 9%2Ax%2B2%2Ay=32

9%2A%284%29%2B2%2A%28-2%29=32 Plug in x=4 and y=-2


36-4=32 Multiply


32=32 Add


32=32 Reduce. Since this equation is true the solution works.


So the solution (4,-2) satisfies 9%2Ax%2B2%2Ay=32


Since the solution (4,-2) satisfies the system of equations


6%2Ax-18%2Ay=60
9%2Ax%2B2%2Ay=32


this verifies our answer.