Answer:
(1, 14)
Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x)=-2x+16\\g(x)=4x+10\end{cases}[/tex]
Substitute the function notation for y to create a system of equations:
[tex]\begin{cases}y=-2x+16\\y=4x+10\end{cases}[/tex]
To find the points of intersection of the given functions, solve the system of equations.
Multiply the first equation (function f(x)) by 2:
[tex]\implies 2y=-4x+32[/tex]
Add this to the second equation (function g(x)) to eliminate x:
[tex]\begin{array}{r l}4x+10 & = y\\+ \quad -4x+32 & = 2y\\\cline{1-2} 42 & = 3y\end{array}[/tex]
Solve for y:
[tex]\implies 3y=42[/tex]
[tex]\implies y=14[/tex]
Substitute the found value of y into one of the equations and solve for x:
[tex]\implies 4x+10=14[/tex]
[tex]\implies 4x=4[/tex]
[tex]\implies x=1[/tex]
Therefore, the point of intersection of the given functions is (1, 14).
