Question

show graphically that the pair of equations 2x-3y+7=0,6x-9y+21=0 has infinitely many solutions​

Answer 1

Answer:

$\boxed{\textsf{ Hence the two lines have infinitely many solutions .}}$

Step-by-step explanation:

We need to prove that , the given lines have Infinitely many Solutions by the graphical method. The given system of equations is ,

$\sf\red{\dashrightarrow}\begin{cases}\sf 2x - 3y +7=0 \\\sf 6x -9y +21=0 \end{cases}$

• For plotting the graph we will need some coordinates of x and y. We can get it by substituting different values of x / y to get the values of x/y .

$\sf\dashrightarrow 2x - 3y + 7 = 0 \\\\\sf\dashrightarrow 2x = 7 + 3y \\\\ \sf\dashrightarrow \boxed{\sf \pink{x = \dfrac{ 7+3y}{2}}}$

Now put on different values of y to get different values of x.

$\boxed{\begin{array}{c|c|c} \sf x &\sf 3.5 &\sf 5 \\ \sf y &\sf 0 &\sf 1 \end{array}}$

Thus , we will plot the points , (3.5,0) and (5,1)

$\rule{200}2$

$\sf\dashrightarrow 6x -9y +21 = 0 \\\\\sf\dashrightarrow 6x = 9y - 21 \\\\\sf\dashrightarrow x =\dfrac{9y-21}{6} \\\\\sf\dashrightarrow \boxed{\sf\pink{ x =\dfrac{3y-7}{2} }}$

Again , put on different values of y to get different values of x.

$\boxed{\begin{array}{c|c|c} \sf x &\sf -3.5 &\sf 5 \\ \sf y &\sf -2 &\sf 1 \end{array}}$

Now when we plot the graph , we see that they concide on each other. Hence they have Infinitely many solutions .