Question

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The graph shows the solution to which system of inequalities?
A) y < x + 1 and y < x - 3
B) y ≤ x + 1 and y > x - 3
C) y ≤ x + 1 and y ≤ x - 3
D) y ≤ x + 1 and y ≥ x - 3

Answer 1

Help

Answer 2

plz

Answer 3

let us take two points on solid line.
Let they be (0,1) and (4,5)
eq. of line through these points is
\[y-1=\frac{ 5-1 }{ 4-0 }(x-0),\left[ y-y1=\frac{ y2-y1 }{ x2-x1 }\left( x-x1 \right) \right]\]
y=x+1
as it is a solid line ,it may be \[\leq~or~\geq.\]
let
\[y \leq x+1\]
let us check (0,0)
\[0 \leq 0+1,0 \leq 1\]
which is true.
hence one eq . is.
\[y \leq x+1\]
repeat the same procedure for second and find the eq.
first any points on the curve are (3,0)and (5,2)
and proceed as above.

Answer 4

What happens next?

Answer 5

\[y-0=\frac{ 2-0 }{ 5-3 }(x-3)=x-3\]
as it is a dotted line so use < or >
let us first use <
y<(x-3)
0<-3
which is not true ,hence (0,0) does not lie on the graph.
But from the graph (0,0) lies on the graph.
Therefore y>x-3
so option is
\[y~ \leq x+1~ and~ y<x-3\]

Answer 6

correction last line y>x-3