20x+5y=120
10x+7.5y=80

1) 20x+5y=120
Stp1: 5y=120-20x
Stp2: 5y=(120/5 and -20x/5)= [y=24-4x]

finding x:
20x+5(24-4x)=120
Stp1: 5*24=120,4x*5=-20
20x+120-20x=120
Stp2: subtract 120 on both sides of = sign
20x-20x=0
Stp3: subtract the variables:
[x=0]
finding y:
20(0)+5y=120
stp1: multiply 20*0
5y=120
stp2: divide 120 by 5
[y=24]

2) 10x+7.5y=80
Stp1: move 7.5y to other sign of =
10x=80-7.5y
Stp2: divide by 10
[x=8-75y]
substitute x and re do original:
stp1: 10(8-75y)+7.5y=80
stp2: 80-7.5y+7.5y=80
stp3: subtract variabled num. with variabled num. and whole num. with whole number: [y=0]

solve for x:
10x-7.5(0)=80
10x=80
[x=8]
check:
10(8)+7.5(0)=80
80+0=80
[80=80]

\( \left \{ {{20x+5y=120} \atop {10x+7.5y=80\ \ | *(-2)}} \right. \\\\ \left \{ {{20x+5y=120} \atop {-20x-14y=-160}} \right. \\+-\\addition\\\\ y=-40\\\\10x=80-7.5y\\\\x=\frac{80-7.5y}{10}=\frac{80-7.5*(-40)}{10}=\frac{80+300}{10}=38 \)


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