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:

$y=2x+4$

$y=-\dfrac{10}{3}x+\dfrac{76}{3}$

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)

$y=-\dfrac{10}{3}x+\dfrac{76}{3}$                  ...(ii)

From (i) and (ii), we get

$2x+4=-\dfrac{10}{3}x+\dfrac{76}{3}$

$2x+\dfrac{10}{3}x=\dfrac{76}{3}-4$

$\dfrac{6x+10x}{3}=\dfrac{76-12}{3}$

Multiply both sides by 3.

$16x=64$

Divide both sides by 16.

$x=\dfrac{64}{16}$

$x=4$

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.