Mathematics

Question

5x+7y=77
5x+3y=53



2x+5y=-1
X+2y=0


3x+6y=6
2x-3y=4

1 Answer

  • 1.)
    [tex]5x+7y=77\\ 5x+3y=53\\ (5x+7y)-(5x+3y)=77-53\\ 5x-5x+7y-3y=24\\ 4y=24\\ y=6\\ 5x+7\cdot 6=77\\ 5x+42=77\\ 5x=77-42\\ 5x=35\\ x=\frac { 35 }{ 5 } \\ x=7[/tex]

    2.)
    [tex]2x+5y=-1\\ x+2y=0\\ \\ 2\cdot (x+2y)=2\cdot 0\\ 2x+4y=0\\ (2x+5y)-(2x+4y)=-1-0\\ 2x-2x+5y-4y=-1\\ y=-1\\ 2x+5\cdot -1=-1\\ 2x-5=-1\\ 2x=-1+5\\ 2x=4\\ x=\frac { 4 }{ 2 } \\ x=2[/tex]

    3.)[tex]3x+6y=6\\ 2x-3y=4\\ 2\cdot (2x-3y)=2\cdot 4\\ 4x-6y=8\\ \\ (3x+6y)+(4x-6y)=6+8\\ 4x+3x+6y-6y=14\\ 7x=14\\ x=\frac { 14 }{ 7 } \\ x=2\\ \\ 3\cdot 2+6y=6\\ 6+6y=6\\ 6y=0\\ y=0\\ [/tex]