Mathematics Multiple Choice Questions on “Linear Equations in Two Variables”.
1. Linear equations are of __________ form.
a) ax2+bx+c = 0
b) ax+by+c = 0
c) x2+y2 = a2
d) x2-y2 = a2
Answer: b
Clarification: Linear equations of two variables are generally denoted by ax+by+c = 0.
Generally, x and y are used as variables however, other letters can be used instead of x and y.
2. How many solutions does a linear equation have?
a) One
b) Two
c) Three
d) Four
Answer: a
Clarification: Let’s understand this by an example:
Suppose we want to find the solution for 9x-3 = 0
9x-3 = 0
9x = 3
Therefore x = 1/3
We can see that this linear equation has only one solution. i.e. x = 1/3
It means that there is only one number which satisfies the given equation.
3. Which of the following is the correct way to represent the equation 3x=9 in ax+by+c = 0 form?
a) 3x = -0y + 9
b) 3x + 0y = 9
c) 3x + 0y – 9 = 0
d) 3x + 0y = 9
Answer: c
Clarification: In ax + by + c = 0, a, b and c are numbers and a, b≠0 while x and y are variables.
Given equation is 3x=9.
If we want it to represent in the ax+by+c=0 form, we can write 3x + 0y – 9 = 0 where a = 3, b = 0 and c = -9.
4. Find the solution for the linear equation 2.5x=5?
a) x=-2
b) x=5
c) x=3
d) x=2
Answer: d
Clarification: 2.5x=5
We know that equations is not affected by dividing the same non-zero number both sides.
Hence, dividing the equation by 2.5 both sides.
Therefore x=5/2.5
Hence, x = 2