Q. 3 A5.0( 3 Votes )

Let us solve the following equations in two variables by the method of substitution and check them graphically.

3x – y = 7

2x + 4y = 0

Answer :

Given 3x – y = 7 … (1)


2x + 4y = 0 … (2)


Expressing y of equation (1) in terms of x,


3x – y = 7


3x - 7 = y … (3)


Substituting (3) in (2),


2x + 4y = 0


2x + 4 (3x – 7) = 0


2x + 12x – 28 = 0


14x – 28 = 0


14x = 28


x = 2


Substituting x value in (3),


3x – 7 = y


3 (2) – 7 = y


y = -1


By solving, we get x = 2 and y = -1.


Justification:


Generally, we substitute x = 0 or y = 0 in the given linear equations to get y and x. So we get two points on the straight line. To find more points on the line, take different values of x related to it, we get different values for y from the equation.


We get the following tables for the given linear equations.


For 3x – y = 7


y = 3x – 7



For 2x + 4y = 0


x = -2y




Plotting these points on a graph and joining them, we get two straight lines.


From the graph, we can see that both lines intersect at (2, -1), hence the solution to this pair is (2, -1).


Hence x and y values satisfy equations (1) and (2).


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