Test: Graphical Solution To Linear Equations - Class 10 MCQ

Pair of linear equations are inconsistent when they are parallel. When the two equations are parallel ,we have .

In D, we have which is , so it is inconsistent.

We have a1, a2 the coefficients of x²,b1 and b2 coefficients of x and c1 and c2 the constant terms.So,a1a2=b1b2c1c2which is a case of parallel lines which which never meet. So there are no solutions obtainable for these equations.

So, they are intersecting lines. And intersecting lines meet at only one point. So only 1 solution is available.

If a  system of two linear equation is consistent system and has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line.So we have which is satisfied by 10x – 14y = -4 only.

To determine which pair is not a solution of the equation 3a+b=12, substitute each pair (a,b) into the equation and check if it satisfies the equation.

1. For (3, 3):

   3(3)+3=9+3=123(3) + 3 = 9 + 3 = 123(3)+3=9+3=12

   This satisfies the equation.

2. For (5, -3):

   3(5)+(−3)=15−3=123(5) + (-3) = 15 - 3 = 123(5)+(−3)=15−3=12

   This satisfies the equation.

3. For (4, 0):

   3(4)+0=12+0=123(4) + 0 = 12 + 0 = 123(4)+0=12+0=12

   This satisfies the equation.

4. For (2, 4):

   3(2)+4=6+4=103(2) + 4 = 6 + 4 = 103(2)+4=6+4=10

   This does not satisfy the equation.

So, the answer is:

1. (2,4)

We have the equations x + 2y – 8 = 0 and 2x + 4y = 16 Where 
Here  which is the case of coincident lines . So there are infinitely many solutions.

Solution: Compare the coefficients of the two equations.

⇒ The ratio of the coefficients of x (a1/a2) = 3/2

⇒ The ratio of the coefficients of y (b1/b2) = 2/(-3) = -2/3

Since 3/2 ≠ -2/3, the lines are consistent.

Therefore, the pair of lines represented by the equations 3x + 2y = 5 and 2x - 3y = 7 are consistent.

The pair of equations has no solutions ,this means that the two equation does not have a common point which means that they does not meet each other anywhere.So the pair of lines which does not meet anywhere are parallel lines and parallel lines are inconsistent.

Linear equation is an equation between two variables that gives a straight line when plotted on a graph. Linear equations have degree 1 only which means that power of the variables is 1 only. Since does not have degree 1 its not a linear equation.

y=0 is x-axis… since every point has y=0. y=-7 is a line parallel to x-axis passing through x=0,y=-7. So the two lines are parallel to each other and are inconsistent which means that it has no solutions because it will never meet.

check ratio
3/5    -2/7   5/2  as they are not equal so unique solution  

 is a case of parallel lines which never meet. So there are no solutions obtainable for these equations. So equations are inconsistent
3x + y = 1, (2K – 1) x + (K – 1) y = 2K + 1
b1=1,b2=k-1,c1=-1,c2=-2k-1

is a case of parallel lines which never meet. So there are no solutions obtainable for these equations. So equations are inconsistent.
3x – y = -8 ,3x – y = 24
3x – y +8=0 ,3x – y -24=0

So, Therefore the equations are inconsistent.

3x – 2y = 4 and 6x – 4y = 8
Putting x=5 and y=3
LHS=3(5)-2(3)
15-6=9
RHS=4
LHS ≠ RHS
Also,
6(5)-4(3)=30-12=18 ≠ 8