Solve and Graph the System of Linear Inequalities below: x ≥ 0 y ≥ 0 y + x ≤ 6 y + 3x ≤ 12 Please show ALL working as much as possible and include in your answer a coordinate pl…

Question

asked May 26, 2020 128k views

1 Answer

Nisal Gunawardana · Answer 1 · 2020-05-30T07:09:16+0000

Answer:

The below graph with portion enclosed by red lines is the solution to the given equations.

Explanation:

$x\geq  0$ means the portion to the right of

$y\geq  0$ means the portion up of the

For
$y + x \leq 6$ , we find
x-interecpt and
y-intercept

For
x-interecpt we substitute y=0

$y+x=6\\0+x=6\\x=6$ ,thus pont is

Similary
y-intercept , we substitute x=0

$y + x= 6\\y+0=6\\y=6$ , thus point is

We connect these these two points and consider the below area as it contains less than inequality

For
$y + 3x\leq 12$ we again find the
x-intercept and
y-intercept

For
x-interecpt we substitute y=0

$y+3x=12\\0+3x=12\\$

divide both side by
, we get

x=4 , thus point is

Similary
y-intercept , we substitute x=0

$y+3x=12\\y+0 =12\\y=12$

Thus point is
,

Now connect these two points and consider the area below the line as it contains less than inequality.

Finally the area enclosed by all these lines is the solution to the given equations, that is shown below.