Question

What is the solution to the following system of equations?

x − 3y = 5
2x + y = 10

(5, 0)
(0, 5)
(7, 0)
(0, 7)

Answer 1

There’s a couple of ways to approach this, but the one I see off the bat is: you can multiply the second equation by 3 to get 3y

From there, you can add the two equations. The -3y and the + 3y will then cancel out and you can solve for x

Answer 2

what do you think it is?

Answer 3

this one I am having trouble figuring out

Answer 4

Try what I suggested: can you multiply the whole second equation by 3 and lmk what you get?

Answer 5

The second equation is:
2x + y = 10

Notice what happens when we multiply everything on both sides by 3

3*2*x + 3*y = 3*10

Equals

6x + 3y = 30

Now our system is:

x − 3y = 5
6x + 3y = 30

Can you try adding the two equations together from here?

Answer 6

I still don't understand :/

Answer 7

The equations:
x − 3y = 5
6x + 3y = 30

Add the x’s: x + 6x = 7x

Add the y’s: -3y + 3y = 0

Add the constants

5+ 30 = 35

So the system is now

7x = 35
X = 5