Question
Solve the inequality graphically in a two-dimensional plane: –3x + 2y $\ge$ – 6
✓
Answer
The given inequality is $ - 3x + 2y \geqslant - 6$.
Draw the graph of the line -3x + 2y = -6
Table of values satisfying the equation -3x + 2y = -6
Draw the graph of the line -3x + 2y = -6
Table of values satisfying the equation -3x + 2y = -6
| X | 2 | 0 |
| Y | 0 | -3 |
Putting (0, 0) in the given in equation, we have $ - 3 \times 0 + 2 \times 0 \geqslant - 6 \Rightarrow 0 \geqslant - 6$ which is true.
$\therefore $ Half plane of $ - 3x + 2y \geqslant - 6$ is towards origin.
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
Find the mean variance and standard deviation for the following data: $15, 22, 27, 11, 9, 21, 14, 9$.
→The mean of $5$ observations is $4.4$ and their variance is $8.24$. If three of the observations are $1, 2$ and $6$, find the other two observations.
→Find the degree measure of the angle subtended at the centre of a circle of radius 100cm by an arc of length 22cm.
How many terms of the sequence $\sqrt{3},3,3\sqrt{3},\ ...$ must be taken to make the sum $39+13\sqrt{3}?$
→Show that A $\cup$B = A $\cap$B implies A = B
→In how many ways can the letters of the word 'ARRANGE' be arranged so that the two R's are never together?
Evaluate the following: $\big(\text{i}^{77}+\text{i}^{70}+\text{i}^{87}+\text{i}^{414}\big)^3$
→How many numbers are there between 1 and 1000 which when divided by 7 leave remainder 4?
If $\text{f(x)}=(\text{a}-\text{x}^\text{n})^{\frac{1}{\text{n}}},\text{a}>0$ and $\text{n}\in\text{N},$ then prove that f(f(x)) = x for all x.
→Find the equation of the hyperbola where foci are (0, $\pm$12) and the length of the latus rectum is $36$.
→