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Page 1
Question:11
Draw the graph of each of the following linear equations in two variables:
i
x + y = 4
ii
x - y = 0
iii
-x + y = 6
iv
Page 2
Question:11
Draw the graph of each of the following linear equations in two variables:
i
x + y = 4
ii
x - y = 0
iii
-x + y = 6
iv
y = 2x
v
3x + 5y = 15
vi
x
2
-
y
3
= 2
vii
x-2
3
= y -3
viii
2y = -x + 1
Solution:
i We are given,
x + y = 4
We get,
y = 4 – x,
Now, substituting x = 0 in y = 4 – x, we get
y = 4
Substituting x = 4 in y = 4 – x, we get
y = 0
Thus, we have the following table exhibiting the abscissa and ordinates of points on the line represented by the
given
x 0 4
y 4 0
Page 3
Question:11
Draw the graph of each of the following linear equations in two variables:
i
x + y = 4
ii
x - y = 0
iii
-x + y = 6
iv
y = 2x
v
3x + 5y = 15
vi
x
2
-
y
3
= 2
vii
x-2
3
= y -3
viii
2y = -x + 1
Solution:
i We are given,
x + y = 4
We get,
y = 4 – x,
Now, substituting x = 0 in y = 4 – x, we get
y = 4
Substituting x = 4 in y = 4 – x, we get
y = 0
Thus, we have the following table exhibiting the abscissa and ordinates of points on the line represented by the
given
x 0 4
y 4 0
i i We are given,
We get,
Now, substituting x = 0 in y = x – 2, we get
Substituting x = 2 in y = x – 2, we get
Thus, we have the following table exhibiting the abscissa and ordinates of points on the line represented by the
given equation
x 0 2
y –2 0
i i i We are given,
We get,
Now, substituting in ,we get
Substituting x = –6 in ,we get
Thus, we have the following table exhibiting the abscissa and ordinates of points on the line represented by the
given equation
x 0 -6
y 6 0
Page 4
Question:11
Draw the graph of each of the following linear equations in two variables:
i
x + y = 4
ii
x - y = 0
iii
-x + y = 6
iv
y = 2x
v
3x + 5y = 15
vi
x
2
-
y
3
= 2
vii
x-2
3
= y -3
viii
2y = -x + 1
Solution:
i We are given,
x + y = 4
We get,
y = 4 – x,
Now, substituting x = 0 in y = 4 – x, we get
y = 4
Substituting x = 4 in y = 4 – x, we get
y = 0
Thus, we have the following table exhibiting the abscissa and ordinates of points on the line represented by the
given
x 0 4
y 4 0
i i We are given,
We get,
Now, substituting x = 0 in y = x – 2, we get
Substituting x = 2 in y = x – 2, we get
Thus, we have the following table exhibiting the abscissa and ordinates of points on the line represented by the
given equation
x 0 2
y –2 0
i i i We are given,
We get,
Now, substituting in ,we get
Substituting x = –6 in ,we get
Thus, we have the following table exhibiting the abscissa and ordinates of points on the line represented by the
given equation
x 0 -6
y 6 0
i v We are given,
Now, substituting x = 1 in ,we get
Substituting x = 3 in ,we get
Thus, we have the following table exhibiting the abscissa and ordinates of points on the line represented by the
given equation
x 1 3
y 2 6
v We are given,
We get,
Page 5
Question:11
Draw the graph of each of the following linear equations in two variables:
i
x + y = 4
ii
x - y = 0
iii
-x + y = 6
iv
y = 2x
v
3x + 5y = 15
vi
x
2
-
y
3
= 2
vii
x-2
3
= y -3
viii
2y = -x + 1
Solution:
i We are given,
x + y = 4
We get,
y = 4 – x,
Now, substituting x = 0 in y = 4 – x, we get
y = 4
Substituting x = 4 in y = 4 – x, we get
y = 0
Thus, we have the following table exhibiting the abscissa and ordinates of points on the line represented by the
given
x 0 4
y 4 0
i i We are given,
We get,
Now, substituting x = 0 in y = x – 2, we get
Substituting x = 2 in y = x – 2, we get
Thus, we have the following table exhibiting the abscissa and ordinates of points on the line represented by the
given equation
x 0 2
y –2 0
i i i We are given,
We get,
Now, substituting in ,we get
Substituting x = –6 in ,we get
Thus, we have the following table exhibiting the abscissa and ordinates of points on the line represented by the
given equation
x 0 -6
y 6 0
i v We are given,
Now, substituting x = 1 in ,we get
Substituting x = 3 in ,we get
Thus, we have the following table exhibiting the abscissa and ordinates of points on the line represented by the
given equation
x 1 3
y 2 6
v We are given,
We get,
Now, substituting x = 0 in ,we get
Substituting x = 5 in ,we get
Thus, we have the following table exhibiting the abscissa and ordinates of points on the line represented by the
given equation
x 0 5
y 3 0
v i We are given,
We get,
Now, substituting x = 0 in ,we get
Substituting x = 4 in ,we get
Thus, we have the following table exhibiting the abscissa and ordinates of points on the line represented by the
given equation
x 0 4
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