how do you solve 2 different equations in the same problem

Question

The problem is as follows. 

Y=4x

X+y=10

Answer 1

Hi Justin,

 

It states that y = 4x in your first equation. So plug 4x into where y is in the second equation.

 

x + y = 10 becomes x + 4x = 10. Which is simplified to 5x = 10 and then x = 2. 

 

Plug 2 in for x in the first equation to get y. y = 4(2) = y = 8

Answer 2

Hi Justin;

Y=4x
X+y=10

In the second equation, the x and y are on the left side.

Let's orient the first equation the same way...

y=4x

Let's subtract 4x from both sides...

-4x+y=0

-(x+y=10)

-5x+0=-10

We are subtracting the second equation from the first...

-5x=-10

x=2

Let's plug this into either equation to solve for y.  I randomly select the first equation...

y=4x

y=(4)(2)

y=8

Let's verify by plugging both results into the second equation...

x+y=10

2+8=10

10=10