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Solve graphically each of the following systems of linear equations. Also, find the coordinates of the points where the lines meet the axis of y:

$x + 2 y − 7 = 0 2 x − y − 4 = 0$

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x = 2 and y = 2 and the coordinates of points where lines meet y axis is (0, 3.5) and (0, -4)

x = 3 and y = 2 and the coordinates of points where lines meet y axis is (0, 3.5) and (0, -4)

x = 3 and y = 3 and the coordinates of points where lines meet y axis is (0, 3.5) and (0, -4)

x = -1 and y = 5 and the coordinates of points where lines meet y axis is (0, 3.5) and (0, -4)

answer is B.

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Detailed Solution

Given equations are

x + 2 y − 7 = 0

…………(1)

2 x − y − 4 = 0

……………(2)
To get the values of x and y, solve equation (1).

x + 2 y = 7

x = 7 − 2 y

…………….(3)
Substitute y = 0 in equation (3).

x = 7 − 20

x = 0

Now, substitute y = 1 in equation (3).

x = 7 − 21

x = 7 − 2

x = 5

Now, substitute y= 3 in equation (3).

x = 7 − 23

x = 7 − 6

x = 1

x	0	1	5
y	0	3	1

To get the values of x and y, solve equation (2).

2 x − y − 4 = 0

2 x = y + 4

x = y + 4 2

……………..(4)
Substitute y = 0 in equation (4).

x = 0 + 4 2

x = 2

Now, substitute y = 1 in equation (4).

x = 1 + 4 2

x = 52

x = 2.5

Now, substitute y= 3 in equation (4).

x = 3 + 4 2

x = 72

x = 3.5

x	2	2.5	3.5
y	0	1	3

Now, form the graph for equation

x + 2 y − 7 = 0

and

2 x − y − 4 = 0

with the obtained values of x and y.
Question Image

As we can observe above, the graphs of the both equations intersect at the point P(3,2).
So, the solution of given two equations are x= 3 and y= 2.
Now, let us calculate the co-ordinates of points where the graphs of the given equations intersect y-axis.
In equation (1), put x=0

0 + 2 y − 7 = 0

2 y = 7

y = 72

y = 0.35

The coordinates of point where equation (1) meet y axis is (0, 3.5).
In equation (2), put x=0.

2 × 0 − y − 4 = 0

− y − 4 = 0

y = − 4

The coordinates of points where equation (2) intersect y axis is (0, -4)
Hence, x=3 and y= 2 and the coordinates of points where lines intersect y axis is (0, 3.5) and (0, -4).
The correct option is (2).

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