What is the solution for 3x + 4y = 10 and 2x + 9y = 20

3x + 4y = 10 

2x + 9y = 20

First, multiply everything in the top equation by 2 and
everything in the second equation by 3

By multiplying, your
equation should look like

6x + 8y = 20

6x + 27y = 60 
now subtract 6x with 6x (which means subtract 8y with 27y and 20 with 60)

By subtracting, your equation should look
like

-19y = -40 divide both
sides by -19

By dividing, your equation should look
like

y = 49/19  which is your
answer for " y "

now plug 40/19 into one of the
equation

By doing that, your equation should look
like

3x + 4 ( 40/19 ) = 10
multiply 40/19 with 4

By multiplying, your equation should
look like

3x + 160/19 = 10
subtract both sides by 160/19

By
subtracting, your equation should look
like

3x = 30/19 now divide
both sides by 3

By dividing, your equation should look
like

x = 10/19 which is your
answer for " x "

So your answer is x = 10/19 
;  y = 40/19