SOLUTION: I submitted this question earlier but there was a typo I apologize to whoever read it. Here it is again. I need to find out how to solve the following problem using the addition o

Algebra ->  Expressions-with-variables -> SOLUTION: I submitted this question earlier but there was a typo I apologize to whoever read it. Here it is again. I need to find out how to solve the following problem using the addition o      Log On


   

Question 119195: I submitted this question earlier but there was a typo I apologize to whoever read it. Here it is again. I need to find out how to solve the following problem using the addition or subtraction property. I need to find the values of x and y in these equations: 9x-2y=15 and 4x+3y=-5. It is very important that I see the work because I want to know exactly how to do it for future problems.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Solving a System of Linear Equations by Elimination/Addition


Lets start with the given system of linear equations

9%2Ax-2%2Ay=15
4%2Ax%2B3%2Ay=-5

In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for y, we would have to eliminate x (or vice versa).

So lets eliminate x. In order to do that, we need to have both x coefficients that are equal but have opposite signs (for instance 2 and -2 are equal but have opposite signs). This way they will add to zero.

So to make the x coefficients equal but opposite, we need to multiply both x coefficients by some number to get them to an equal number. So if we wanted to get 9 and 4 to some equal number, we could try to get them to the LCM.

Since the LCM of 9 and 4 is 36, we need to multiply both sides of the top equation by 4 and multiply both sides of the bottom equation by -9 like this:

4%2A%289%2Ax-2%2Ay%29=%2815%29%2A4 Multiply the top equation (both sides) by 4
-9%2A%284%2Ax%2B3%2Ay%29=%28-5%29%2A-9 Multiply the bottom equation (both sides) by -9


So after multiplying we get this:
36%2Ax-8%2Ay=60
-36%2Ax-27%2Ay=45

Notice how 36 and -36 add to zero (ie 36%2B-36=0)


Now add the equations together. In order to add 2 equations, group like terms and combine them
%2836%2Ax-36%2Ax%29-8%2Ay-27%2Ay%29=60%2B45

%2836-36%29%2Ax-8-27%29y=60%2B45

cross%2836%2B-36%29%2Ax%2B%28-8-27%29%2Ay=60%2B45 Notice the x coefficients add to zero and cancel out. This means we've eliminated x altogether.



So after adding and canceling out the x terms we're left with:

-35%2Ay=105

y=105%2F-35 Divide both sides by -35 to solve for y



y=-3 Reduce


Now plug this answer into the top equation 9%2Ax-2%2Ay=15 to solve for x

9%2Ax-2%28-3%29=15 Plug in y=-3


9%2Ax%2B6=15 Multiply



9%2Ax=15-6 Subtract 6 from both sides

9%2Ax=9 Combine the terms on the right side

cross%28%281%2F9%29%289%29%29%2Ax=%289%29%281%2F9%29 Multiply both sides by 1%2F9. This will cancel out 9 on the left side.


x=1 Multiply the terms on the right side


So our answer is

x=1, y=-3

which also looks like

(1, -3)

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

9%2Ax-2%2Ay=15
4%2Ax%2B3%2Ay=-5

we get



graph of 9%2Ax-2%2Ay=15 (red) 4%2Ax%2B3%2Ay=-5 (green) (hint: you may have to solve for y to graph these) and the intersection of the lines (blue circle).


and we can see that the two equations intersect at (1,-3). This verifies our answer.