Solutions To Linear Equations - Free MCQ Practice Test with solutions,

The solution of the linear equation is represented by the ordered pair (x,y)

Hence if x>0 , y>0 , then the solution will always lie in the first quadrant.

Put the given points in the equation 3x + 2y = 6

If L.H.S of the equation is equal to R.H.S

then the given points will lie on the line

3x + 2y = 6

3.0 + 2.3 = 6

6 =6 

L.H.S = R.H.S

So the given point lie on the line. 

Upstream = (x-y) km/hr

Downstream =(x+y)km/hr

20(x+y)=2

X+Y=10.....(1)

4(x-y)=2

x-y=2....(2)

Solve both equations

x+y=10

x-y=2

2x=12

X=6

Substitute x=6in i

6+y=10

Y=4

Speed of rowing in still water is 6km/hr.

the speed of still water is 4km/hr

So option B is correct answer. 

In the given question we have  a=3,b=1 the given equation is 2a + 3b=m

By substituting the values of a,b in the given  equation, we get ,

 2 x 3 + 3 x 1 = m 

6 + 3 = m

9 = m 

So option A is the correct answer. 

Given equation is :

-0.25x + 1.3 = -0.55x – 0.2

-0.25x + 0.55x = -0.2 - 1.3

0.30 x = -1.5

So x = -1.5 / 0.30

x = -5

So option B is correct answer. 

The point will lie on the line if L.H.S of the equation is equal to R.H.S

Given equation is 2x - y = 5

Put the point ( 2 , -1) in the above equation

2 . 2 - (-1) = 4 + 1 = 5 = R.H.S

So this proves that the given points lie on the line. 

So option D is correct answer.  

Given Equations

ax + by = 3    {1}

3a - 2b = 1     {2}

x = 2, y = 1 ( given) 

Equation {1} becomes,

2a + b = 3      {3}

Substract equation {3} from {2}, we get,

2a + b - 3a + 2b = 3 - 1

-a + 3b  = 2

3b = 2 + a

b = (2+a) / 3 

Put the value of b in equation {3}, we get

2a + (2 +a ) / 3 = 3

(6a +a +2) / 3 = 3

7a + 2 = 9

a = 1

Now put value of a in {3}

2 + b = 3

b = 1

hence we get value of a and b i.e. 1 and 1 

Given equation is :

4x + 3y = 16

Putting x = 1 and y = 4 

4 .1 + 3. 4 = 16

4 + 12 = 16

16 = 16 

So option D is the correct answer.

Given that the equation 3x + ay = 8 passes through the point (2,2) it means that (2,2) is a solution of the equation 

Putting X= 2 and Y = 2 in the equation we have  
3(2) + a (2) = 8
6 + 2a = 8
2a = 8-6
2a = 2
a = 2/2 = 1
Therefore value of
a = 1

So option D is correct answer.