Question

How do you solve $y = 2x$ and $3x - 2y = - 2$?

Answer 1

Hint: All the given equations above are linear equations; therefore we will solve the equations by the method of elimination by subtracting the equations to reduce the variables in it.

Complete step-by-step solution:
We have the equations as:
Equation $(1)$ can be written as: $y = 2x \to (1)$
Equation $(2)$ can be written as: $3x - 2y = - 2 \to (2)$
Now since there is only $1$ variable in equation $(1)$ therefore there is no need to use the elimination method, we can directly substitute equation $(1)$ in equation $(2)$ as:
We know that $y = 2x$, on substituting this in the expression $3x - 2y = - 2$, we get:
$ \Rightarrow 3x - 2(2x) = - 2$
Now on simplifying the term, we get:
$ \Rightarrow 3x - 4x = - 2$
On further simplifying we get:
$ \Rightarrow - x = - 2$
On rearranging the terms in the equation, we get:
$ \Rightarrow x = 2$, which is the value of $x$.
Now to get the value of $y$, we will substitute $x = 2$ in equation $(1)$ as:
$ \Rightarrow y = 2(2)$
On simplifying we get:
$ \Rightarrow y = 4$, which is the value of $y$.

Therefore, the values of $x$ and $y$ are $2$ and $4$ respectively, which is the required solution.

Note: To check whether the solution is correct we have to test the values of $x$ and $y$ in equation $(2)$
On substituting the values in the left-hand side of the equation, we get:
$ \Rightarrow 3(2) - 2(4)$
On simplifying we get:
$ \Rightarrow 6 - 8$
Which is equal to $ - 2$ , which is the right-hand side, therefore the solution is correct.
It is to be remembered that in any given equation multiplying or dividing the equation by a specific constant doesn’t change the value of the equation.
In the given question we had two variables which are $x$ and $y$, therefore they can be solved by using elimination, where there are more than three variables, and the matrix is used to solve them.