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]

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