Solve the given system by substitution.

Question

{-4p+q=-5

{p-q=7

Answer 1

-4p + q = -5

   p  - q =  7

 

p = 7 + q  from the second equation.

Substitute into the first equation : -4(7 + q) + q = -5

-28 -4q + q = -5  ⇔ -3q = 23 ⇒ q = -23/3

Substitute into the second equation : p = -23/3  + 21/3  p = -2/3  

Answer 2

Solving by substitution means to solve one equation in terms of one variable and place that value for the selected variable into the second equation. 

 

If you solve the second equation for the variable q, you find that q=p-7

 

Next take this value for q and place in into the first equation wherever there is a q.

 

-4p+p-7=-5

 

Now the equation only has one unknown variable and can be solved.

 

p= -2/3

 

Now that you have p you can find the value of q. 

-2/3-q=7

So q=-23/3

 

 

Answer 3

You need to set one equation equal to one of the variables and then plug that into the other.

 

Eq 2: p = 7 +q

 

Eq1:

-4(7+q) + q = -5

-28 - 4q +q = -5

-3q = 23

q = -23/3

 

Now plug that back into equation 2.

 

p - (-23/3) = 7

p = 7 - 23/3

p = 21/3 - 23/3

p = -2/3