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Pair of Linear Equations in Two Variables

Short Answer Type

181. Check, whether, x = 5 and y = —2 is a solution of the system of simultaneous linear equations 2x + 3y = 4 and 3x + 5y = 5. Also state whether system is consistent or inconsistent.

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182. Check whether, x = 4, y = 5 and x = 2, y = 7.5 are solutions of the system of equation

straight x over 2 plus straight y over 5 equals 3

nd 10x + 4y = 50. Also, state, whether system is consistent or inconsistent.

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183. Tanvika goes to Monday market with her brother Nimit to have “Gol-gappa” and “dahi-bhalla”. They took number of plates of “gol-gappa” twice that of “dahi-bhalla”. The cost of one plate of gol-gappa was Rs. 5 and cost of one plate of dahi-bhalla was Rs. 10. They spent Rs. 60 which they had spent for market. Represent the situation algebraically.

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184. Pankaj Jain is three times as old as his son. In 12 years time, he will twice as old as his son. Represent the situation algebraically.

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185. Romila went to a stationary shop and purchased 2 pencils and 3 erasers for Rs 9. Her friend Sonali saw the new variety of pencils and erasers with Romila and she also bought 4 pencils and 6 erasers of the same kind for Rs. 18. Represent the situation algebraically.

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186. If x = 2, y = 4, find the value of p when 7x - 4y = p.

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187. Manish says to Rahim “I am three times as old as you are.” Later Manish says to Rahim “After 5 years I shall be two times as old as you will be.” Represent this situation algebraically and graphically.

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Long Answer Type

188.
Represent the following system of linear equations graphically from the graph find the points where the lines intersect y-axis.

3x + y - 5 = 0, 2x - y - 5 = 0

We have,
3x + y - 5 = 0
⇒ y = 5 - 3x
Thus we have following table :
We have,3x + y - 5 = 0⇒ y = 5 - 3xThus we have following table :
We

We have, 2x - y - 5 = 0
⇒ y = 2x - 5
Thus, we have following table :
We have,3x + y - 5 = 0⇒ y = 5 - 3xThus we have following table :
We

Fig. 3.19.

When we plot the graph of the given equation, we find that both the lines intersect at the point (-1, 2), therefore x = -1, y = 2 is the solution of the given system of equations.
From the graph we observe that lines intersect y-axis at (-5, 0) and (5,0)

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189. Determine vertically the co-ordinates of vertices of the triangle formed by the lines whose equations are y = x, y = 2x and x + y = 6.

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190.

Draw the graphs of the equations :
x - y = 1
and 2x + y = 8
Determine the vertices of the triangle formed by these lines and x-axis.

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