Question

1/2x+1/4y=6. 1/5x+1/3y=1

Answer 1

1st Step:


`\frac { 1 }{ 2 } x+\frac { 1 }{ 4 } y=6\\ \\ 4\left( \frac { 1 }{ 2 } x+\frac { 1 }{ 4 } y \right) =6\cdot 4\\ \\ 2x+y=24\\ \\ y=24-2x`

2nd Step:


`\frac { 1 }{ 5 } x+\frac { 1 }{ 3 } y=1\\ \\ 15\left( \frac { 1 }{ 5 } x+\frac { 1 }{ 3 } y \right) =1\cdot 15`


`\\ \\ 3x+5y=15\\ \\ 5y=15-3x\\ \\ 5y=3\left( 5-x \right) \\ \\ y=\frac { 3\left( 5-x \right) }{ 5 }`

3rd Step:


`\frac { 3\left( 5-x \right) }{ 5 } =24-2x`


`\\ \\ 5\cdot \frac { 3\left( 5-x \right) }{ 5 } =5\left( 24-2x \right) \\ \\ 3\left( 5-x \right) =120-10x`


`\\ \\ 15-3x=120-10x\\ \\ -3x+10x=120-15\\ \\ 7x=105\\ \\ x=\frac { 105 }{ 7 }`


`\\ \\ \therefore \quad x=15`

4th Step (When x=15):


`y=24-2\left( 15 \right) \\ \\ y=24-30\\ \\ \therefore \quad y=-6`

Answer 2

`(1)/(2)x+(1)/(4)y=6 \ \ \ |* 2 \\ (1)/(5)x+(1)/(3)y=1 \ \ \ |* (-5) \\ \\ x+(1)/(2)y=12 \\ \underline{-x-(5)/(3)y=-5} \\ (1)/(2)y-(5)/(3)y=12-5 \\ (3)/(6)y-(10)/(6)y=7 \\ -(7)/(6)y=7 \\ y=7 * (-(6)/(7)) \\ y=-6 \\ \\ x+(1)/(2)y=12 \\ x+(1)/(2) * (-6)=12 \\ x-3=12 \\ x=12+3 \\ x=15 \\ \\ \boxed{(x,y)=(15,-6)}`