Hi Lindsay;
4x+3y=24
5x+y=19
Let's isolate one variable.
The second equation is easier.
5x+y=19
Let's add 5x to both sides...
5x5x+y=5x19
y=5x19
Let's plug this into the first equation...
4x+3y=24
4x+[(3)(5x19)]=24
Let's distribute the 3 within the brackets...
4x+(15x57)=24
4x+15x57=24
Let's combine like terms...
11x57=24
Let's add 57 to both sides...
57+11x57=24+57
11x=33
Let's divide both sides by 11...
(11x)/11=33/11
x=3
Let's plug this into either equation to establish y. I randomly select the first...
4x+3y=24
[(4)(3)]+3y=24
12+3y=24
3y=12
y=4
Let's plug both values into the second equation to verify...
5x+y=19
[(5)(3)]+(4)=19
154=19
19=19
It works!
Jan 27

Vivian L.