Question

Y=2x + 4 y= -10/3 x + 76/3 what is the sum of the x- and y-values in the solution to the system of equations?

Answer 1

Given:

The system of equations:

`y=2x+4`

`y=-(10)/(3)x+(76)/(3)`

To find:

The sum of the x- and y-values in the solution to the system of equations.

Solution:

We have,

`y=2x+4` ...(i)

`y=-(10)/(3)x+(76)/(3)` ...(ii)

From (i) and (ii), we get

`2x+4=-(10)/(3)x+(76)/(3)`

`2x+(10)/(3)x=(76)/(3)-4`

`(6x+10x)/(3)=(76-12)/(3)`

Multiply both sides by 3.

`16x=64`

Divide both sides by 16.

`x=(64)/(16)`

`x=4`

Putting x=4 in (i), we get

`y=2(4)+4`

`y=8+4`

`y=12`

The solution of system of equations is (4,12).

`x+y=4+12`

`x+y=16`

Therefore, the sum of the x- and y-values in the solution to the system of equations is 16.