Question

Determine the value of b if (-1,10) is a solution of the equation 3x+by =27. Also find the coordinates of the point on its graph for which x=7 .

Answer 1

Step-by-step explanation:

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hope it helps you dear friend

Answer 2

$\large\underline{\sf{Solution-}}$

Given equation of line is

$\rm :\longmapsto\:3x + by = 27 - - - (1)$

It is given that the point (- 1, 10) is the solution of line (1).

Therefore,

$\rm :\longmapsto\:3( - 1) + b(10) = 27$

$\rm :\longmapsto\: -3+10 b = 27$

$\rm :\longmapsto\: 10 b = 27 + 3$

$\rm :\longmapsto\: 10 b = 30$

$\rm :\longmapsto\: b = 3$

So,

Equation (1) can be rewritten as

$\rm :\longmapsto\:3x + 3y = 27$

$\rm :\longmapsto\:3(x + y) = 27$

$\rm :\longmapsto\:x + y = 9 - - - - (2)$

Substituting 'x = 0' in the given equation, we get

$\rm :\longmapsto\:0 + y = 9$

$\rm :\longmapsto\: y = 9$

Substituting 'y = 0' in the given equation, we get

$\rm :\longmapsto\:x + 0 = 9$

$\rm :\longmapsto\:x= 9$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 9 \\ \\ \sf 9 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (0 , 9) & (9 , 0)

➢ See the attachment graph.

From graph we concluded that,

when x = 7 then y = 2