Question

solve the following systems
6x + 3y = 6
8x + 5y = 12
please show work if you can!

Answer 1

Let's use the 'elimination by addition and subtraction' method. Take the first equation
6x + 3y = 6
and divide every one of these three terms by -3. what do you get?

Next, plese take the second equation: 8x + 5y = 12, and divide all of these three terms by 5. What do you get?

type out your results.

Answer 2

to use substitution
divide equation 1 by 3 to get 2x + y = 2
y = 2-2x
substitute in equation 2
8x + 5(2-2x) = 12
solve for x
use this value of x in y = 2-2x

good practice to check your solution by putting in either of original equations

Answer 3

@mathmale to use that method it is always better to "match" to coefficient of the variable you want to eliminate. you do not have to let the coefficient = 1 and have to work with fractions etc.
for this problem multiply the first equation by 5 so when you subtract the y's cancel out
10x -8x = 10 - 12

Answer 4

To continue Triciaal's excellent answer, you could have, instead,
1. multiply the entire first equation by 5
(the coefficient of y in the second equation)
2. multiply the entire second equation by 3
(the coefficient of y in the first equation)

This gives us:

30x + 15y = 30
24x + 15y = 36

Subtract, and we get

6x = -6

and I bet you can finish it from here.

The nice thing about math is that there are usually multiple ways to get to the same answer.