algebra
posted by Sue .
if 5 times the first number plus 3 times the second number equals 47 and 10 times the first number minus 4 times the second number equals 54, what are the numbers?
please explain the steps

5x + 3y = 47
10x  4y = 54
substitution:
5x = 47  3y, so 10x = 946y, thus
10x4y = 946y  4y = 54
10y = 40
y=4
so, x = 7
elimination:
multiply the first equation by 4 and the 2nd by 3
20x+12y = 188
30x12y = 162
add them, and the y's go away:
50x = 350
x=7
so, y=4