Respuesta :
Consider the equation y=f(x), with solutions of the form (x,y)
y=f(x) means that y equals an expression in terms of x,
for example f(x) could be [tex] -5x^{2}+7x-1 [/tex], or [tex] 8\sqrt{x}- \frac{7}{x} [/tex]
so f(x) is an expression with x'es and numbers
Given 2 equations:
i) y=f(x) and g) y=g(x)
the solutions of the system:
i. y=f(x)
ii. y=g(x)
are pairs (x,y) which satisfy both i and ii, at the same time.
to solve this system, we let f(x)=g(x).
In our problem, we are given: [tex] \frac{1}{3}(x-2)= \frac{1}{4}(x+11) [/tex]
since both expressions are expressions of x and some numbers,
let
[tex]f(x)=\frac{1}{3}(x-2)[/tex] and [tex]g(x)=\frac{1}{4}(x+11)[/tex]
then a system of equations is:
i) [tex]y=\frac{1}{3}(x-2)[/tex]
ii) [tex]y=\frac{1}{4}(x+11)[/tex]
Remark:
to find the solutions:
[tex]\frac{1}{3}(x-2)= \frac{1}{4}(x+11)[/tex]
4(x-2)=3(x+11)
4x-8=3x+33
x=33+8=41
to find y substitute x=41 in either of the equations:
for x=41, y=1/3 (x-2) = 1/3 (41-2) =1/3 (39) = 13
[or y= 1/4 (x+11) = 1/4 (41+11)= 1/4 (52) = 13
