Given:
The system of equations:
[tex]y=2x+4[/tex]
[tex]y=-\dfrac{10}{3}x+\dfrac{76}{3}[/tex]
To find:
The sum of the x- and y-values in the solution to the system of equations.
Solution:
We have,
[tex]y=2x+4[/tex] ...(i)
[tex]y=-\dfrac{10}{3}x+\dfrac{76}{3}[/tex] ...(ii)
From (i) and (ii), we get
[tex]2x+4=-\dfrac{10}{3}x+\dfrac{76}{3}[/tex]
[tex]2x+\dfrac{10}{3}x=\dfrac{76}{3}-4[/tex]
[tex]\dfrac{6x+10x}{3}=\dfrac{76-12}{3}[/tex]
Multiply both sides by 3.
[tex]16x=64[/tex]
Divide both sides by 16.
[tex]x=\dfrac{64}{16}[/tex]
[tex]x=4[/tex]
Putting x=4 in (i), we get
[tex]y=2(4)+4[/tex]
[tex]y=8+4[/tex]
[tex]y=12[/tex]
The solution of system of equations is (4,12).
[tex]x+y=4+12[/tex]
[tex]x+y=16[/tex]
Therefore, the sum of the x- and y-values in the solution to the system of equations is 16.
