Answer:
The equation which the graph of the system of equation solve is:
Option: a [tex]\dfrac{-1}{2}x+3=3x-4[/tex]
Step-by-step explanation:
It is given that:
On the graph there is two linear functions intersecting at (2, 2
)
This means that both the equations i.e. the equation on left and right hand side of the equality must pass through (2,2)
i.e. when x=2 the value of the expression must be 2.
b)
[tex]\dfrac{-1}{2}x-3=-3x+4[/tex]
on taking left hand side
[tex]\dfrac{-1}{2}x-3[/tex]
when x=2 we get:
[tex]=\dfrac{-1}{2}\times 2-3\\\\\\=-1-3\\\\\\=-4\neq 2[/tex]
Hence, option: b is incorrect.
c)
[tex]\dfrac{1}{2}x+3=3x+4[/tex]
on taking left hand side
[tex]\dfrac{1}{2}x+3[/tex]
when x=2 we get:
[tex]=\dfrac{1}{2}\times 2+3\\\\\\=1+3\\\\\\=4\neq 2[/tex]
Hence, option: c is incorrect.
d)
[tex]\dfrac{1}{2}x+3=-3x-4[/tex]
on taking left hand side
[tex]\dfrac{1}{2}x+3[/tex]
when x=2 we get:
[tex]=\dfrac{1}{2}\times 2+3\\\\\\=1+3\\\\\\=4\neq 2[/tex]
Hence, option: d is incorrect.
Hence, we are left with option: a
a)
[tex]\dfrac{-1}{2}x+3=3x-4[/tex]
on taking left hand side
[tex]\dfrac{-1}{2}x+3[/tex]
when x=2 we have:
[tex]=\dfrac{-1}{2}\times 2+3\\\\\\=-1+3\\\\\\=2[/tex]
Also, on taking the right hand side
[tex]3x-4[/tex]
when x=2 we have:
[tex]=3\times 2-4\\\\\\=6-4\\\\\\=2[/tex]
Hence, it passes through (2,2)
