SOLUTION: Can someone please help me with this problem? Solve the system by addition. –2x + 5y = –19 x – 3y = 10

Algebra ->  Expressions-with-variables -> SOLUTION: Can someone please help me with this problem? Solve the system by addition. –2x + 5y = –19 x – 3y = 10       Log On


   

Question 124252: Can someone please help me with this problem?
Solve the system by addition.
–2x + 5y = –19
x – 3y = 10
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
-2x+%2B+5y+=+-19
x-3y+=+10

Multiply the 2nd equation by 2 so that the coefficients on the x terms are additive inverses.

-2x+%2B+5y+=+-19
2x-6y+=+20

Now add the two equations, term-by-term, to get:

0x-y=1

And solve for y

-y=1
y=-1

Go back to your original two equations:
-2x+%2B+5y+=+-19
x-3y+=+10

Multiply the first by 3 and the second by 5:
-6x+%2B+15y+=-57
5x-15y+=+50

Again, add term-by-term
-x%2B0y=-7

x=7

So the solution set of the system is the ordered pair (7,-1)

Check your answer:
Does the solution set make both equations true statements?
-2%287%29+%2B+5%28-1%29+=+-14-5=-19 yes
7+-3%28-1%29+=+7+%2B+3+=+10 yes

Further check, graph the system. Do the graphs intersect at (7,-1)?

graph%28400%2C400%2C-2%2C8%2C-8%2C2%2Cx%2F3-%2810%2F3%29%2C%282x%29%2F5-%2819%2F5%29%29

Looks like it to me.