Question
Solve the following systems of inequations graphically: $5\text{x}+\text{y}\leq10,2\text{x}+2\text{y}\geq12,\text{x}+4\text{y}\geq12,\text{x}\geq0,\text{y}\geq0$
✓
Answer
We have,
$5\text{x}+\text{y}\leq10,2\text{x}+2\text{y}\geq12,\text{x}+4\text{y}\geq12,\text{x}\geq0,\text{y}\geq0$
Converting the inequations into equations, we obtain,
5x + y = 10, 2x + 2y = 1, x + 4y = 12, x = 0 and y = 0
Region represented by $5\text{x}+\text{y}\geq1$
Putting x = 0 in 5x + y = 10, we get y = 10
Putting y = 0 in 5x + y = 10, we get $\text{x}=\frac{10}{5}=2$
$\therefore$ The line 5x + y = 10, meets the coordinate axes at (0, 10) and (2, 0). Join these points by a thick line.
Now, putting x = 0 and y = 0 in $5\text{x} + \text{y} \geq 10,$ we get $0\geq10,$ This is not possible.
$\therefore$ (0, 0) does not satisfies the inequality $5\text{x} + \text{y} \geq 10,$. so, the portion not containing the origin is represented by the inequation $5\text{x} + \text{y} \geq 10,$
Region represented by 2x + 2y > 12:
Putting x = 0 in 2x +2y = 12, we get $\text{y}=\frac{12}{2}=6$
Putting y = 0 in 2x + 2y = 12, we get $\text{x}=\frac{12}{2}=6$
The line 2x + 2y = 12 meets the coordinate axes at (0, 6) and (6, 0). Join these point by a thick line.
Now, putting x = 0 and y = 0 in 2x + 2y = 12, we get $0\geq12,$ which is not possible. Therefore, (0, 0) does not satisfies the inequality 2x + 2y = 12. so, the portion not containing the origin is represented by the inequation 2x + 2y = 12.
Region represented by $\text{x}+4\text{y}\geq12$
Putting x = 0 in x + 4y = 12, we get $\text{y}=\frac{12}{4}=3$
Putting y = 0 in x + 4y = 12, we get x = 12.
$\therefore$ The line x + 4y = 12 meets the coordinate axes at (0, 3) and (12, 0). Join these points by a thick line.
Now, putting x = 0 and y = 0 in x + 4y = 12, we get $0\geq12,$ which is not possible.
Therefore, (0, 0) does not satisfies the inequality $\text{x}+4\text{y}\geq12$ so, the portion not containing the origion is represented by the inequation $\text{x}+4\text{y}\geq12$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Show that for any sets A and B,$\text{A}\cup(\text{B}-\text{A})=(\text{A}\cup\text{B})$
→Solve the system of inequality graphically: x – 2y $\le$ 3, 3x + 4y $\ge$ 12, x $\ge$ 0 , y $\ge$ 1
→Calculate the mean, median and standard deviation of the following distribution:
| Class-interval: | 31-35 | 36-40 | 41-45 | 46-50 | 51-55 | 56-60 | 61-65 | 66-70 |
| Frequency: | 2 | 3 | 8 | 12 | 16 | 5 | 2 | 3 |
The line 2x + 3y = 12 meets the x-axis at A and y-axis at B. The line through (5, 5) perpendicular to AB meets the x-axis and the line AB at C and E respectively. If O is the origin of coordinates, find the area of figure OCEB.
Reduce each of the following expressions to the sine and cosin of a single expression: $\cos\text{x}-\sin\text{x}$
→If $\cos\text{x}-\sin\text{x}=\text{a}^3, \sec\text{x}-\cos\text{x}=\text{b}^3,$ than proved that $a^2b^2 (a^2 + b^2) = 1$.
→Find sets A, B and C such that $\text{A}\cap\text{B},\text{ A}\cap\text{C and B}\cap\text{C}$ are non-empty sets and $\text{A}\cap\text{B}\cap\text{C}=\phi.$
→Find the equation of the parabola, if The focus is at $(0, -3)$ and the vertex is at $(-1, -3)$.
→Evaluate the following limits in Exercise:$\lim\limits_{\text{x}\rightarrow0}\frac{\sin{\text{ax}}}{\text{bx}}$
→Represent to solution set of each of the following inequations graphically in two dimensional plane: $3\text{x}-2\text{y}\leq\text{x}+\text{y}-8$
→