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

1 Answer
Tony B
May 29, 2016

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

x=1
y=4

Explanation:

Given:
color(blue)(y=4x) ..................................(1)
color(brown)(x+y=5)................................(2)

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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.

color(brown)(x+y=5" "->" "x+color(blue)(4x)=5)color(white)(..)...................(2_a)

But 4x+x=5x

x+4x=5" "->" "5x=5

Divide both sides by 5

5/5xx x = 5/5

But 5/5=1

x=1
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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

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

In algebra 4x is the same as 4 xx x

But x has the value of 1 so we have

y=4xx1

y=4
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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

Tony B

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