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Mathematics : Linear Equations in Two Variables

Short Answer Type

201.

Consider the point A(–2, 3)

(i) How many lines can be drawn passing through A?
(ii) Give equation of any two lines passing through A.
(iii) Without actually drawing the graph, find a point, other than A, on each of these two lines.

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202.

(i) Express y in terms of x in the equation

2x–3y = 12.
(ii) Draw its graph.
(ii) Find the co-ordinates of the points where the line cuts the x-axis and y-axis.

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203. Draw the graphs of y = x and y = –x in the same axes. Also, find the co-ordinates of the point where the two lines intersect.

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204. Express y in terms of x in the equation 5x - 4y + 20 = 0. Draw the graph and find the points where the lines represented by this equation cuts x-axis and y-axis.

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205. Draw the graph of 3x + y = 6. At what points, does the graph intersect the axes?

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206. Let y vary directly as x. If y = 12 when x = 4, then write a linear equation. Draw the graph of this linear equation. Check if the point (5, 15) lies on the graph.

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207. Draw the graph of the equations 3x + 4y = 7 and 3x – 2y = 1 and find the point of intersection of lines representing the equations.

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208. Find the value of k if x = 2, y = 1 is a solution of the equations 2x +3y = k and 3x + y = k.

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209. Give the equations of two lines passing through (–3, 4). How many more such lines are possible?

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210. The cost of a pen is र 6 more than two times the cost of a pencil. Write a linear equation in two variables to represent this statement and draw the graph of the linear equation obtained.

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