SOLUTION: could you show me how to graph this; Solve the system by addition. 5x – 4y = –5 x – 2y = –7 The answer I got was x-3; y=5 Thank you so much!

Algebra ->  Systems-of-equations -> SOLUTION: could you show me how to graph this; Solve the system by addition. 5x – 4y = –5 x – 2y = –7 The answer I got was x-3; y=5 Thank you so much!      Log On


   

Question 117018: could you show me how to graph this;
Solve the system by addition.
5x – 4y = –5
x – 2y = –7
The answer I got was x-3; y=5
Thank you so much!
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

5%2Ax-4%2Ay=-5
1%2Ax-2%2Ay=-7

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 5 and 1 to some equal number, we could try to get them to the LCM.

Since the LCM of 5 and 1 is 5, we need to multiply both sides of the top equation by 1 and multiply both sides of the bottom equation by -5 like this:

1%2A%285%2Ax-4%2Ay%29=%28-5%29%2A1 Multiply the top equation (both sides) by 1
-5%2A%281%2Ax-2%2Ay%29=%28-7%29%2A-5 Multiply the bottom equation (both sides) by -5


So after multiplying we get this:
5%2Ax-4%2Ay=-5
-5%2Ax%2B10%2Ay=35

Notice how 5 and -5 add to zero (ie 5%2B-5=0)


Now add the equations together. In order to add 2 equations, group like terms and combine them
%285%2Ax-5%2Ax%29-4%2Ay%2B10%2Ay%29=-5%2B35

%285-5%29%2Ax-4%2B10%29y=-5%2B35

cross%285%2B-5%29%2Ax%2B%28-4%2B10%29%2Ay=-5%2B35 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:

6%2Ay=30

y=30%2F6 Divide both sides by 6 to solve for y



y=5 Reduce


Now plug this answer into the top equation 5%2Ax-4%2Ay=-5 to solve for x

5%2Ax-4%285%29=-5 Plug in y=5


5%2Ax-20=-5 Multiply



5%2Ax=-5%2B20 Subtract -20 from both sides

5%2Ax=15 Combine the terms on the right side

cross%28%281%2F5%29%285%29%29%2Ax=%2815%29%281%2F5%29 Multiply both sides by 1%2F5. This will cancel out 5 on the left side.


x=3 Multiply the terms on the right side


So our answer is

x=3, y=5

which also looks like

(3, 5)

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

5%2Ax-4%2Ay=-5
1%2Ax-2%2Ay=-7

we get



graph of 5%2Ax-4%2Ay=-5 (red) 1%2Ax-2%2Ay=-7 (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 (3,5). This verifies our answer.