Question
Find at least $3$ solutions for the linear equation $2x – 3y + 7 = 0.$
✓
Answer
$2 x-3 y+7=0$
$\Rightarrow 3 y=2 x+7$
$\Rightarrow y=\frac{2 x+7}{3}$
Put $x =0$, then $y=\frac{2(0)+7}{3}=\frac{7}{3}$
Put $x =1$, then $y=\frac{2(1)+7}{3}=3$
Put $x =2$, then $y=\frac{2(2)+7}{3}=\frac{11}{3}$
Put $x=3$, then $y=\frac{2(3)+7}{3}=\frac{13}{3}$
$\therefore\left(0, \frac{7}{3}\right),(1,3),\left(2, \frac{11}{3}\right)$ and $\left(3, \frac{13}{3}\right)$ are the solutions of the equation $2 x-3 y+7=0$.
$\Rightarrow 3 y=2 x+7$
$\Rightarrow y=\frac{2 x+7}{3}$
Put $x =0$, then $y=\frac{2(0)+7}{3}=\frac{7}{3}$
Put $x =1$, then $y=\frac{2(1)+7}{3}=3$
Put $x =2$, then $y=\frac{2(2)+7}{3}=\frac{11}{3}$
Put $x=3$, then $y=\frac{2(3)+7}{3}=\frac{13}{3}$
$\therefore\left(0, \frac{7}{3}\right),(1,3),\left(2, \frac{11}{3}\right)$ and $\left(3, \frac{13}{3}\right)$ are the solutions of the equation $2 x-3 y+7=0$.
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
A sphere, a cylinder, and a cone have the same diameter. The height of the cylinder and also the cone are equal to the diameter of the sphere. Find the ratio of their volumes.
If $a^2+b^2+c^2=16$ and $a b+b c+c a=10$, find the value of $a+b+c$
→How many solution$(s)$ of the equation $2x + 1 = x – 3$ are there on the:
$i.$ Number line
$ii.$ Cartesian plane?
→$i.$ Number line
$ii.$ Cartesian plane?
Find all the angles of an equilateral troiangle.
In fig the side $A B$ and $A C$ of $\triangle A B C$ are produced to point $E$ And $D$ respectively. If bisector $B O$ and $C O$ of $\angle C B E$ And $\angle B C D$ respectively meet at point $O$, then prove that $\angle B O C=90^{\circ}-\frac{1}{2} \angle B A C$
→The angles of a quadrilateral are in the ratio $3 : 5 : 9 : 13$. Find all the angles of the quadrilateral.
→Ten observations $6, 14, 15, 17, x + 1, 2x - 13, 30, 32, 34, 43$ are written in an ascending order. The median of the data is$ 24.$ Find the value of$ x.$
→A joker's cap is in the form of a right circular cone of base radius $7\ cm$ and height $24\ cm$. Find the area of the sheet required to make $10$ such caps. $\Big(\text{Use}\ \pi=\frac{22}{7}\Big).$
→Show that the quadrilateral formed by joining the mid-points the sides of a rhombus, taken in order, form a rectangle.
Given below are the seats won by different political parties in the polling oucome of a state assembly elections:
Draw a bar graph to represent the polling results.
→|
Political party
|
$A$
|
$B$
|
$C$
|
$D$
|
$E$
|
$F$
|
|
Seats won
|
$65$
|
$52$
|
$34$
|
$28$
|
$10$
|
$31$
|