# How do you solve y=4x and x+y=5?

May 29, 2016

The common point for these two equations ( where the graphs cross) is:

$x = 1$
$y = 4$

#### Explanation:

Given:
$\textcolor{b l u e}{y = 4 x}$ ..................................(1)
$\textcolor{b r o w n}{x + y = 5}$................................(2)

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To solve for a variable your equation has to end up with just 1 of that variable and no others. That variable has to be on one side of the equals sign and everything else on the others side.

If we substitute for y in equation (2) using what y is worth from equation (1) we have just 1 variable. Which is $x$.

$\textcolor{b r o w n}{x + y = 5 \text{ "->" } x + \textcolor{b l u e}{4 x} = 5} \textcolor{w h i t e}{. .} \ldots \ldots \ldots \ldots \ldots \ldots . \left({2}_{a}\right)$

But $4 x + x = 5 x$

$x + 4 x = 5 \text{ "->" } 5 x = 5$

Divide both sides by 5

$\frac{5}{5} \times x = \frac{5}{5}$

But $\frac{5}{5} = 1$

$x = 1$
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Substitute for $x$ in equation (1) where $x = 1$

color(brown)(y=4x" "->" "y=4(color(blue)(1))

In algebra $4 x$ is the same as $4 \times x$

But $x$ has the value of 1 so we have

$y = 4 \times 1$

$y = 4$
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Note that $x + y = 5$ is another way of writing
$y = - x + 5$