solve by substitution

Question

y=-2x-8

-4x-y=24

Answer 1

y = -2x - 8     ;     -4x - y = 24

 

the substitution method requires that you solve one of the given equation for one of the unknown variables in term of the other variable and substitute it into the other given equation and that would leave you with an equation with only one unknown variable which you can now solve for and then you can solve for the other variable.

 

here, you already have the first part worked out for you. they have solved one of the equation for y. that is, you have an equation which is solved for y in terms of x ==>   y = -2x - 8

 

substitute  "-2x - 8"   for y in the other equation:

 

     -4x - y = 24

     -4x - (-2x - 8) = 24

 

the  "-"  sign needs to be distributed into each term inside the set of parentheses that follows it, which would yield the following:

 

     -4x -(-2x) - (-8) = 24

     -4x + 2x + 8 = 24

 

combine the like terms on the left hand side of the equation:

 

     -4x + 2x + 8 = 24

     -2x + 8 = 24

 

subtract 8 from both sides to get the following:

 

     -2x + 8 - 8 = 24 - 8

     -2x = 16

 

divide by -2 to solve for x:

 

     -2x/-2 = 16/-2     ==>     x = -8

 

now that we've solve for x, we can substitute its value into the first equation:

 

     y = -2x - 8

     y = -2(-8) - 8

     y = 16 - 8

     y = 8 

Answer 2

Hi Buruca,

 

Since the first equation is already solved for y, you can simply plug it into the second equation wherever you see a y.

 

y=-2x-8

and

-4x-y=24  

 

-------

 

-4x - (-2x-8) =24

 

Now you should be able to solve for x.  When you have an answer for x, plug it into the following equation to find the value for y, y=-2x-8.

 

Let me know if you are still having trouble with this problem.