Question

How do you solve $y = x - 2$ and $y = 4x + 1$ ?

Answer 1

In this question, a linear equation of two variables is given. Here we will use the substitution method to solve these two linear equations. To solve the equations using the substitution method, we should follow the below steps:
-Select one equation and solve it for one of its variables.
-On the other equation, substitute for the variable that we get from the first step.
-Solve the new equation.
-Substitute the value that we found into any equation involving both variables and solve for the other variable.
-Check the solution in both original equations.

Complete step by step answer: Here, we want to solve the equations using the substitution method.
$\Rightarrow y = x - 2$ ...(1)
$\Rightarrow y = 4x + 1$ ...(2)
In the first step, on the other equation, substitute for the variable that we get from the first step.
Substitute $y = x - 2$ in equation (2).
$\Rightarrow x - 2 = 4x + 1$
Let us subtract 4x on both sides.
$\Rightarrow x - 4x - 2 = 4x - 4x + 1$
Now, simplify the above equation.
$\Rightarrow - 3x - 2 = 1$
Now, let us add 2 on both sides.
$\Rightarrow - 3x - 2 + 2 = 1 + 2$
Now, simplify the above equation.
$\Rightarrow - 3x = 3$
Let us divide both terms by -3.
$\Rightarrow \dfrac{{ - 3x}}{3} = \dfrac{3}{{ - 3}}$
That is equal to,
$\Rightarrow x = - 1$
Now, put the value of x in equation (1).
$\Rightarrow y = x - 2$
Put the value of x.
$\Rightarrow y = - 1 - 2$
That is equal to
$\Rightarrow y = - 3$
Hence, we find the value of x is -1 and the value of y is -3 using substitution methods.

Note:
To check whether our answer is correct or not, feed the x and y values in each equation.
Let us take equation (1) and put the values.
$\Rightarrow y = x - 2$
Put $x = - 1$ and $y = - 3$ .
$\Rightarrow - 3 = - 1 - 2$
Now, apply addition on the right-hand side.
That is equal to,
$\Rightarrow - 3 = - 3$
Now, let us take equation (2) and put the values.
$\Rightarrow y = 4x + 1$
Put $x = - 1$ and $y = - 3$ .
$\Rightarrow - 3 = 4\left( { - 1} \right) + 1$
Now, apply multiplication on the right-hand side.
$\Rightarrow - 3 = - 4 + 1$
That is equal to,
$\Rightarrow - 3 = - 3$