Question

Solve this system of equations: $4x + 3y = 1$ and $x = 1 - y$?

Answer 1

Hint: Here we will proceed by taking the second equation from the pair and substitute it into another equation from the given pair of equations, it will give the value of one variable. After that substitute the value in the first equation to get the value of the second variable. Thus, we will get the required values of the equation.

Complete step by step answer:
Linear pairs of equations are equations that 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-
$ \Rightarrow 4x + 3y = 1$ --------(1)
$ \Rightarrow x = 1 - y$ ------(2)
Now we will put the value of x from equation (2) in equation (1),
$ \Rightarrow 4\left( {1 - y} \right) + 3y = 1$
Open the bracket and multiply the terms,
$ \Rightarrow 4 - 4y + 3y = 1$
Add the terms on the left side,
$ \Rightarrow 4 - y = 1$
Move constant term on one side,
$ \Rightarrow - y = - 3$
Multiply both sides by $-1$,
$ \Rightarrow y = 3$
Here we will substitute the value of y in equation (2) to get the value of $x$,
$ \Rightarrow x = 1 - 3$
Simplify the terms,
$\therefore x = - 2$
Hence, the values of x and y are -2 and 3 respectively.

Note: This question primarily focuses on solving by the method of substitution but there can be another method to solve problems involving two linear equations in two variables. It is the elimination, in this method the coefficients of a specific variable of both the equations are made the same and then eliminated using basic operations of addition or subtraction. The other variable which is non-eliminated is taken out. The eliminated variable can be taken out using this variable obtained.