Feasible Solution

Q. Write $\sqrt{7}y=2x$ as a linear equation of the form ax + by + c = 0. Also, write the values corresponding to a, b, c. Does the graph of this linear equation pass through origin? Give your answer in 'yes' or 'no'.

Q.

In the figure given below, If
A
B
∥
C
D
and
C
D
∥
E
F
and y : z = 3 : 7, find x. [4 MARKS]

Q. Find the value of k for which the point (1, −2) lies on the graph of the linear equation x − 2y + k = 0.

Q.

Which of the following are feasible solutions for a linear programming problem with constraints
x ≥0, y ≥ 0
3x+5y ≤ 15
5x+2y ≤ 10

1. (1, -1)

2. (-3, 5)

3. (0, 0)

4. (2, 0)

Q.

Find some ordered pairs of the linear equation 2x+y=4 and plot them how many

such ordered pairs can be found and plotted?

Q. Find the equation of the plane which passes through the point (3, 4, −1) and is parallel to the plane 2x − 3y + 5z + 7 = 0. Also, find the distance between the two planes.

Q.

Which of the following are feasible solutions for a linear programming problem with constraints
x ≥0, y ≥ 0
3x+5y ≤ 15
5x+2y ≤ 10

1. (1, -1)

2. (-3, 5)

3. (0, 0)

4. (2, 0)

Q. Find the value of k for which the point (1, −2) lies on the graph of the linear equation x − 2y + k = 0.

Q. If $\text{U}$ is a set of all triangles in a plane and set $\text{A}$ is the set of triangles with atleast one angle different from ${60}^{\circ }$, then ${\text{A}}^{\prime }$ is a set of ______ triangles.

1. equilateral
2. isosceles
3. scalene
4. right-angled