Question

Solve the following pair of linear equations by substitution method:
3x + 2y – 7 = 0
4x + y – 6 = 0

Answer 1

Hint- Here we will proceed by taking one of the equations from the pair and convert it into a third equation. Then we will substitute the newly formed equation into another equation from the given pair of equations. Hence we will get the required values of the equation.

Complete step-by-step answer:

Linear pairs of equations are equations which can be expressed as ax + by + c = 0 where a, b and c are real numbers and both a, b are non-zero.
In this question, two equations are-
3x + 2y – 7 = 0…………. (1)
4x + y – 6 = 0………. (2)
Firstly, we will take equation 2 and convert it –
4x + y – 6 = 0………. (2)
Or 4x + y = 6
Or y = 6 – 4x………. (3)
Now we will put the value of y i.e. equation 3 in equation 1 i.e. 3x + 2y – 7 = 0 -
3x + 2(6 – 4x) – 7 = 0
Or 3x + 12 – 8x – 7 = 0
Or 5 – 5x = 0
Or 5x = 5
Or x = 1
Here we will substitute the value of x in equation 3 i.e. y = 6 – 4x to get value of y-
y = 6 – 4(1)
or y = 6 – 4
or y = 2
Hence values of x and y are 1 and 2 respectively.

Note- In order to solve this type of question, we must know all the steps mentioned above. Also in the step where we substituted the value of one variable (here x) in equation 3, we can also substitute this value in equation 1 or equation 2 also.