SOLUTION: Solve the following system of equations. 2 x - 5 y = -13 3 x+ 2 y = 9 Answer: (x, y) =

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Solve the following system of equations. 2 x - 5 y = -13 3 x+ 2 y = 9 Answer: (x, y) =      Log On


   

Question 1178174: Solve the following system of equations.
2 x - 5 y = -13
3 x+ 2 y = 9
Answer: (x, y) =
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849) 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

2%2Ax-5%2Ay=-13
3%2Ax%2B2%2Ay=9

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 2 and 3 to some equal number, we could try to get them to the LCM.

Since the LCM of 2 and 3 is 6, we need to multiply both sides of the top equation by 3 and multiply both sides of the bottom equation by -2 like this:

3%2A%282%2Ax-5%2Ay%29=%28-13%29%2A3 Multiply the top equation (both sides) by 3
-2%2A%283%2Ax%2B2%2Ay%29=%289%29%2A-2 Multiply the bottom equation (both sides) by -2


So after multiplying we get this:
6%2Ax-15%2Ay=-39
-6%2Ax-4%2Ay=-18

Notice how 6 and -6 add to zero (ie 6%2B-6=0)


Now add the equations together. In order to add 2 equations, group like terms and combine them
%286%2Ax-6%2Ax%29-15%2Ay-4%2Ay%29=-39-18

%286-6%29%2Ax-15-4%29y=-39-18

cross%286%2B-6%29%2Ax%2B%28-15-4%29%2Ay=-39-18 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:

-19%2Ay=-57

y=-57%2F-19 Divide both sides by -19 to solve for y



y=3 Reduce


Now plug this answer into the top equation 2%2Ax-5%2Ay=-13 to solve for x

2%2Ax-5%283%29=-13 Plug in y=3


2%2Ax-15=-13 Multiply



2%2Ax=-13%2B15 Subtract -15 from both sides

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

cross%28%281%2F2%29%282%29%29%2Ax=%282%29%281%2F2%29 Multiply both sides by 1%2F2. This will cancel out 2 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)

2%2Ax-5%2Ay=-13
3%2Ax%2B2%2Ay=9

we get



graph of 2%2Ax-5%2Ay=-13 (red) 3%2Ax%2B2%2Ay=9 (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.



Answer: (x,y) =(1,3)

Answer by ikleyn(52752) About Me  (Show Source):
You can put this solution on YOUR website!
.

Special note for @MathLover1: 

    There in NO worst way to teach as to use these pluggable solvers.