Solve the system of equations.

10y+7x=29

-5y-9x=2

We multiply the 2nd equation by 2 so that you can get 10 in the first part

It will be

10y+7x=29

-10-18x=4

Now we can cancel out both of the 10s (not caring what sign they are)

Now we are left with

+7x=29

-18x=4

Then we check the sign if the signs of the equations. If they are different we add both of the equations. If they are the same we subtract.

In our case we add, so we end up with

+7-18 = 29+4

-11x=33

So we bring - 11 to the other side. It will become + 11. The we will get x=33/11 which makes x=3

Then we use the first equation and replace x with 3

So

10y+21 (7*3) = 29

10y+21=29

We bring 21 to the other side and subtract it from 29

10y = 8

Then we bring 10 to the other side and then divide it

y=8/10

y=0.8

You can also check by doing 10y+7x=?

10*0.8 + 7*3 =

8 + 21 = 29

So x=3

y=0.8