# Solving Using Substitution

• Nov 29th 2011, 12:31 PM
annon25
Solving Using Substitution
Hey Everyone! I'm going to have a few emergency help questions today and early tomorrow. I have a huge test.(Doh)

My problem right now is solving with substitution, and I am given the following problem to do so with:

4x+y=5
2x-3y=13

I'm thinking I should bring up the 2x or the 3 from the bottom equation to the top? T

Thanks!
• Nov 29th 2011, 12:35 PM
Quacky
Re: Solving Using Substitution
Rearranging the first to isolate $\displaystyle y$:

$\displaystyle y=5-4x$
Now attempt to substitute this into the second equation. If you can't, then please show your working.
• Nov 29th 2011, 01:18 PM
pickslides
Re: Solving Using Substitution
Multiply the second equation through by 2 then subtract the result from the first equation.
• Nov 29th 2011, 01:26 PM
Soroban
Re: Solving Using Substitution
Hello, annon25!

Quote:

Solve by substitution: .$\displaystyle \begin{array}{cccc}4x+y&=&5 & [1] \\ 2x-3y&=&13 & [2]\end{array}$

I'm thinking I should bring up the 2x or the 3 from the bottom equation to the top?
What does that mean?

Do you understand the substitution method?

[1] Solve one of the equations for one of its variables.
[2] Substitute this into the other equation and solve for the remaining variable.
[3] Then solve for the other variable.

Solve [1] for $\displaystyle y\!:\;\;y \:=\:5-4x$

Substitute into [2]: .$\displaystyle 2x - 3(5-4x) \:=\:13$

. . . . and we have: .$\displaystyle 2x - 15 + 12x \:=\:13 \quad\Rightarrow\quad 14x \:=\:28 \quad\Rightarrow\quad x \,=\,2$

Substitute into [1]: .$\displaystyle 4(2) + y \:=\:5 \quad\Rightarrow\quad y \,=\,\text{-}3$

Therefore: .$\displaystyle \begin{Bmatrix}x &=& \;2 \\ y &=& \text{-}3 \end{Bmatrix}$

• Nov 29th 2011, 01:28 PM
e^(i*pi)
Re: Solving Using Substitution
Quote:

Originally Posted by annon25
Hey Everyone! I'm going to have a few emergency help questions today and early tomorrow. I have a huge test.(Doh)

My problem right now is solving with substitution, and I am given the following problem to do so with:

4x+y=5
2x-3y=13

I'm thinking I should bring up the 2x or the 3 from the bottom equation to the top? T

Thanks!

Since the questions states substitution I would not use pickslide's methods (which is elimination). What it wants you to do is sub an expression for either x or y into the other equation solving for one of the variables then finding the other.

In your case it is easier to subtract 4x from both sides to get $\displaystyle y = 5-4x$. You can now sub 5-4x for y in the second equation: $\displaystyle 2x-3(5-4x) = 13$.

You can now find x and then use the first equation to find y
• Nov 29th 2011, 01:32 PM
annon25
Re: Solving Using Substitution
Okay,
This is what I ended up with:

2x-4x-3y

If I plug in 2 as x and-3 as y, I am getting the answer "5..."
• Nov 29th 2011, 01:35 PM
e^(i*pi)
Re: Solving Using Substitution
Quote:

Originally Posted by annon25
Okay,
This is what I ended up with:

2x-4x-3y

If I plug in 2 as x and-3 as y, I am getting the answer "5..."