How do you solve a System of Equations using the Substitution Method?

Question

For example:

p+q = 4

4p+q = 1

How would you solve that?

Answer 1

solve the top eqn. for q
q=4-p
Now sub 4-p in for q in the second eqn.
4p +4-p = 1
3p+4=1
3p=-3
p=-1

q = 4 -( -1) = 5

Answer 2

You want to solve for one of the unknowns in the simplest equation.

Using p + q = 4, you can solve for q and get q = 4 - p.

By substitution, enter 4 - p in for q in the other equation:

4p + q = 1
4p + 4 - p = 1
3p + 4 = 1
3p = -3
p = -1

Now you have solved for p. You can now solve for q by putting your value for p back into one of the equations. I"m going to choose the most simple one:

p + q = 4
-1 + q = 4
q = 5.

Answer 3

Solve the first equation for one of the variables:

p = 4 - q

Substitute this value into the second equation and solve for the other variable:

4(4 - q) +q = 1
16 - 4q + q = 1
16 - 3q = 1
3q = 15
q = 5

Substitute this value back into the first equation and solve for the first variable:

p + 5 = 4
p = 4 - 5
p = -1

Answer 4

1) p+q = 4 ISOLATE ONE OF THE VARIABLES.
-q -q
2) p = 4-q
3) 4(4-q) + q = 1 PLUG IN THE P (which is already equal to 4-q)
4) 16-4q+q = 1 DISTRIBUTE the 4 into the parenthases.
5) 16-3q = 1 ADD THE COMMON VARIABLES.
6) -3q = -15 DIVIDE by -3 on both sides.
7) q = 5 Now you have solved for q.

Now all you have to do is plug in 5 for q to solve for p. I hope I helped and didn't just confuse you more. I tend to do that when explaining things. =)

Answer 5

p+q= 4 means q = 4-p (a)

you put this value of q in the second equation

4p+4-p =1

3p=-3 p=-1 and in a you find q=5

result p = -1 q=5

Answer 6

So in the top problem solve for p, you won't eliminate any variables yet. p= -q+4

Now where ever you see p in the next equation put in -q+4 in parenthesizes so now it's 4( -q+4)+q=1

Distribute the 4 into the parenthesizes - 4q+16+q=1

Solve for q... ------> q=5

Put 5 in for q in the first equation and solve for p.... p+5=4

So p = -1 and q = 5

Answer 7

Start with the first equation, and rewrite it in terms of p or q:

p = 4-q (rewritten in terms of q)

Since we now know p in terms of q, substitute the expression 4-q for p in the second equation:

4(4-q)+q = 1 and solve for q

q = 5

Now plug q into the first equation and solve for p:

p+5 = 4
p = -1

That's it!

Answer 8

You solve the first equation for q

p+q=4
-p__-p
q=4-p

then you plug in that equation for Q in the second equation

4p+(4-p)=1
4p+4-p=1
solve
3p=-3
p=-1

then you plug p=-1 into the first equation
-1+q=4
solve
q=5

plug it in to check

Answer 9

p+q = 4 subtract p from both sides
q=4-p
4p+q = 1 substitute 4-p for q
4p+4-q=1 combime like terms
3p+4=1 subtract 4 from each side
3p=-3 divide both sides by 3
p=-1
q=4-p substitute -1 for p
q=4-(-1)
q=5
(-1, 5)

Answer 10

p+q =4: q = 4-p (sub this into the second equation for q
4p+q =1
4p + 4-p = 1
3p +4 =1
3p = -3
p = -1
q = 4-(-1)
q = 5
(-1,5)