Conditions
Category : 9th Class
For pair of linear equations in two variable is......
\[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\]
\[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\]
(i) If \[\frac{{{a}_{1}}}{{{a}_{2}}}\ne \frac{{{b}_{1}}}{{{b}_{2}}}\] then lines are intersecting.
(ii) If \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}}\] then lines are coincident.
(iii) If\[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}\ne \frac{{{c}_{1}}}{{{c}_{2}}}\] then lines are parallel.
Solve for \[\mathbf{x}\] and y; graphically.
\[x-y-1=0\]
\[2x+y-8=0\]
Solution:
We have
\[x-y-1=0\] ....(i)
\[\Rightarrow \]\[x=y+1\]
\[x\] | 1 | 2 | 3 |
Y | 0 | 1 | 2 |
Now locate the points (1, 0), (2, 1) and (3, 2) on the graph paper and draw a line passing through it
\[2x+y-8=0\] \[\Rightarrow \]\[y=8-2x\]
\[x\] | 1 | 2 | 3 |
Y | 6 | 4 | 2 |
Now locate the point (1, 6), (2, 4) and (3, 2) on the same graph and draw another line passes through these points
In the graph the coordinate of point of intersection is (3, 2). Therefore, \[x=3\] and y = 2 is the solution of given pair of linear equations.
Which one of the following options is correct?
(a) Linear equation in two variable is in the form of \[\text{a}x+\text{by}+\text{c}=0\], where \[\text{a}=0\]
(b) Linear equation in two variable is in the form \[px+q\text{y}+\text{c}=0\]
(c) Linear equation is in the form of \[sx+t\text{y}+r=0\], where s, r and t are constants and s, \[t\ne 0\]
(d) Linear equation in three variable is \[ax+b\text{y}+c=0\], where a, b, c are constants and a,\[b\ne 0\]
(e) None of these
Answer: (c)
Explanation:
Compare with the general formula, it is clear that option (c) is correct.
Which one of the following statements is false?
(a) The equation of x-axis is y = 0
(b) The equation of y-axis is \[x=0\]
(c) The equation of a line parallel to x-axis at a distance a from origin is \[x=a\]
(d) The equation of a line which is parallel to y-axis at a distance a from origin be \[x=a\]
(e) None of these
Answer: (c)
Explanation:
Option (c) is false because equation of required line will be y = a
The area bounded by y-axis, \[2x+3y=12\] and \[x-y=1\] is.... .
(a) 7.5 square unit
(b) 13.5 square unit
(c) 4.5 square unit
(d) 75 square unit
(e) None of these
Answer: (a)
In the following pair of linear equation the value of \[x\] and y is \[2x+3y=-5\] and \[3x-2y=12\]:
(a) (2, 3)
(b) (-2,-3)
(c) (-2, 3)
(d) (2, 3)
(e) None of these
Answer: (d)
The coordinate of points where lines \[x+3y-6=0\] and \[2x-3y-12=0\] intersect y-axis:
(a) (0, 2), (-4, 0)
(b) (2, 0), (0, -4)
(c) (0, 2), (0, -4)
(d) (0, 2), (-4, 0)
(e) None of these
Answer: (c)
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