Question

Solve this system of linear equaiton by an algebraic method.

So If I had to solve this the elimination method way, how would I do it?

x-2y = 10
3x-y = 0

Answer 1

x - 2y = 10
3x - y = 0

eliminate y by multiplying 3x - y = 0 by -2

-2(3x - y = 0) = -6x + 2y = 0

ADD the 2 equations
x - 2y = 10
-6x + 2y = 0
-5x + 0 = 10
-5x = 10
x = -2

substitute x = -2 in x - 2y = 10, to find y

x - 2y = 10
-2 - 2y = 10
-2y = 12
y = -6

check x = -2, y = -6
3x - y = 0
3(-2) - -6 = 0
-6 + 6 = 0
0 = 0

Answer 2

Oh so You have to multiply it by -2 because the first equation also uses -2 and you have to cancel them out that way right?

So if its - and + that means you have to add the equations. If its - and - that means you have to subtract and if it's + and + that also means you have to subtract right?

How did you get -2 as an answer?
Did you divide 5x by 5 and 10 by five to get 2?

You lost me right here:
How did you do this?

x - 2y = 10
-2 - 2y = 10
-2y = 12
y = -6

How did you get the second line?
-2 - 2y = 10?

And at the end you went 0 = 0
so they have to equal to zero always?

Answer 3

How did you get -2 as an answer?
Did you divide 5x by 5 and 10 by five to get 2? YES

You lost me right here:
How did you do this?

x - 2y = 10
-2 - 2y = 10
-2y = 12
y = -6

How did you get the second line?
-2 - 2y = 10?

to find the value of y, since you know x = -2, you plug x = -2 into either equation and solve for y

the second line is from plugging -2 in for x in the equation x - 2y = 10

x = -2
x - 2y = 10
-2 - 2y = 10
-2y = 12
y = -6

yes, when you check, both sides will equal 0 if you are correct