Hi Angelica;
5x+y=9 and 10x7y=18
The coefficients of x are 5 and 10. To apply the practice of elimination, we want only one coefficient.
Let's take the first equation...
5x+y=9
Let's multiply both sides by 2...
2(5x+y)=(9)(2)
10x+2y=18
Let's subtract this from the second equation...
10x7y=18
(10x+2y=18)
10x10x=0
7y2y=9y
1818=36
09y=36
The x is eliminated.
9y=36
Let's divide both sides by 9...
(9y)/9=36/9
A negative number divided by a negative number has a positive result...
y=4
Let's plug this into either equation to establish the value of x. I randomly select the second...
10x7y=18
10x[(7)(4)]=18
10x28=18
Let's add 28 to both sides...
28+10x28=18+28
10x=10
Let's divide both sides by 10...
(10x)/10=10/10
x=1
Let's plug both values into the first equation to verify results...
5x+y=9
[(5)(1)]+4=9
5+4=9
9=9
2/3/2014

Vivian L.