equations

x-6y=10 and 2x-2y=10     Multiply BOTH sides of the first eq by -2 to get

12y-2x=-20     then add to the second equation to get

10y = -10

y=-1

 

Sustitute y=-1 into one of the equations

x- 6(-1) = 10

x+6 =10

x=4

$x-6y=10$  $2x-2y=10$

 

There are two ways to do it: by substitution and by subtraction

 

By substitution using the first equation first:

 

$x-6y=10$

 

$x=10+6y$

 

Substitute the $x$ in the second equation with $10+6y$

 

$2(10+6y)-2y=10$

 

$20+12y-2y=10$

 

$20+10y=10$

 

$10y=-10$

 

$y=-1$

 

Substitute the $y$ in the first equation with $-1$

 

$x-6(-1)=10$

 

$x+6=10$

 

$x=4$

 

$(-1,4)$

 

OR

 

Substitute the $y$ in the second equation with $-1$

 

$2x-2(-1)=10$

 

$2x+2=10$

 

$2x=8$

 

$x=4$

 

$(-1,4)$

 

By substitution using the first equation second:  

 

$x-6y=10$

 

$-6y=10-x$

 

$y=\frac{10-x}{-6}$

 

Substitute the $y$ in the second equation with $\frac{10-x}{-6}$

 

$2x-2(\frac{10-x}{-6})=10$

 

$2x+\frac{10-x}{3}=10$

 

$\frac{10-x}{3}=10-2x$

 

$10-x=30-6x$

 

$-x=20-6x$

 

$-x+6x=20$

 

$5x=20$

 

$x=4$

 

Substitute the $x$ in the first equation with $4$

 

$4-6y=10$

 

$-6y=6$

 

$y=-1$

 

$(4,-1)$

 

OR

 

Substitute the $x$ in the second equation with $4$

 

$2(4)-2y=10$

 

$8-2y=10$

 

$-2y=2$

 

$y=-1$

 

$(4,-1)$

 

By substitution using the second equation first:

 

$2x-2y=10$

 

$2x=10+2y$

 

$x=\frac{10+2y}{2}$

 

$x=5+y$

 

Substitute the $x$ in the first equation with $5+y$

 

$5+y-6y=10$

 

$5-5y=10$

 

$-5y=5$

 

$y=-1$

 

Substitute the $y$ in the second equation with $-1$

 

$2x-2(-1)=10$

 

$2x+2=10$

 

$2x=8$

 

$x=4$

 

$(4,-1)$

 

OR

 

Substitute the $y$ in the first equation with $-1$

 

$x-6(-1)=10$

 

$x+6=10$

 

$x=4$

 

$(4,-1)$

 

By subtracton by subtracting the second equation from the first equation:

 

     $x-6y=10$

-  $2x-2y=10$

--------------------------

   $-x-4y=0$

 

$-x=0+4y$

 

$-x=4y$

 

$x=-4y$

 

Substitute the $x$ in the first equation with $-4y$

 

$-4y-6y=10$

 

$-10y=10$

 

$y=-1$

 

Substitute the $y$ in the second equation with $-1$

 

 

$2x-2(-1)=10$

 

$2x+2=10$

 

$2x=8$

 

$x=4$

 

$(4,-1)$

 

OR

 

Substitute the $x$ in the second equation with $-4y$

 

$2(-4y)-2y=10$

 

$-8y-2y=10$

 

$-10y=10$

 

$y=-1$

 

Substitute the $y$ in the first equation with $-1$

 

$x-6(-1)=10$

 

$x+6=10$

 

$x=4$

 

$(4,-1)$

 

By subtracton by subtracting the first equation from the second equation:

 

  $2x-2y=10$

-  $x-6y=10$

--------------------------

   $x+4y=0$

 

$x=0-4y$

 

$x=-4y$

 

Substitute the $x$ in the first equation with $-4y$

 

$-4y-6y=10$

 

$-10y=10$

 

$y=-1$

 

Substitute the $y$ in the second equation with $-1$

 

 

$2x-2(-1)=10$

 

$2x+2=10$

 

$2x=8$

 

$x=4$

 

$(4,-1)$

 

OR

 

Substitute the $x$ in the second equation with $-4y$

 

$2(-4y)-2y=10$

 

$-8y-2y=10$

 

$-10y=10$

 

$y=-1$

 

Substitute the $y$ in the first equation with $-1$

 

$x-6(-1)=10$

 

$x+6=10$

 

$x=4$

 

$(4,-1)$