Answer:
y > -2/3x + 2, y [tex]\geq[/tex] x
[tex]\left \{ {{y > -2/3x + 2} \atop {y \geq x}} \right.[/tex]
Step-by-step explanation:
Knowledge Needed
A system of linear inequalities is graphing 2 lines.
If the line's y side is less than it's x-side (y </ [tex]\leq[/tex] x), shade below.
If the line's y side is greater than it's x-side (y </ [tex]\leq[/tex] x), shade above.
If the line is dotted, it is < or >.
If the line is filled in, it is [tex]\leq[/tex] or [tex]\geq[/tex].
Where both regions are shaded is the solution.
Question
Examine the dotted line.
1) We know it is < or > because it is dotted.
2) We know it is y > .... because if it was less than, it would be shaded below, which is impossible because the shaded region is above.
3) We know the y-intercept, when x=0, is 2.
4) We know the slope, how much the y-value of a line changed when the x-value changes by 1, is -2/3.
y > -2/3x + 2
Examine the solid line.
1) We know it is [tex]\geq[/tex] or [tex]\leq[/tex] because it is solid.
2) We know it is y [tex]\geq[/tex] .... because if it was less than, it would be shaded below, which is impossible because the shaded region is above.
3) We know the y-intercept, when x=0, is 0.
4) We know the slope, how much the y-value of a line changed when the x-value changes by 1, is 1.
y [tex]\geq[/tex] 1x + 0
y [tex]\geq[/tex] x
The solution to the linear inequality is when both lines are shaded in (true), which means both lines are the solution together.
y > -2/3x + 2, y [tex]\geq[/tex] x
