Question

How do you solve the system of equations: $y = 2x + 1$ and $y = 4x - 1$

Answer 1

We are given a pair of linear equations and we have to find the value of x and y by using the given equation. We can solve the equation by the method of elimination or by using the method of substitution for the method of substitution. First we will find the value of one variable in the form of another for example we will find the value of x in terms of y then substitute that value in another equation. Then we will solve the equation and find the value of that variable. After that, substitute the value of that variable in the other equation and find the value of the remaining one variable.

Complete step-by-step answer:
Step 1: We are given a pair of linear equations $y = 2x + 1$ and $y = 4x - 1$ by applying the method of substitution we will find the value of both variables. Substitute the value of $y$ from first equation to the second equation:
$\Rightarrow 2x + 1 = 4x - 1$
Subtracting $4x$ from both sides:
$\Rightarrow 2x + 1 - 4x = 4x - 1 - 4x$
On proper rearrangement we will get:
$\Rightarrow - 2x + 1 = - 1$
Step2: Now we will subtract $1$ from both sides.
$\Rightarrow - 2x + 1 - 1 = - 1 - 1$
On proper rearrangement we will get:
$\Rightarrow - 2x = - 2$
Dividing both sides by $- 2$ we get:
$\Rightarrow \dfrac{{ - 2x}}{{ - 2}} = \dfrac{{ - 2}}{{ - 2}}$
$\Rightarrow x = 1$
Step 3: Now we will substitute the value of $x$ into the first equation to find the value of $y$:
$\Rightarrow y = 2\left( 1 \right) + 1$
On simplifying the equation we get:
$\Rightarrow y = 2 + 1$
$\Rightarrow y = 3$

Hence the solution of the pair of linear equations is $x = 1$ and $y = 3$.

Note:
This type of question we can solve by the method substitution. In this method, the main thing is to find the value of one variable in terms of other students mainly doing the mistakes here.