Question

How do you solve the system of equations by using substitution \[x - 2y = 0\] and \[2x - 5y = - 4\]?

Answer 1

Hint: In this question we are asked to find the solution by using a substitution method, in this method first convert the equation in terms of only one variable by using one of its equation and substitute the obtained value in one of its equations to get the other value.

Complete step by step solution:
Substitution method can be defined as a way to solve a linear system of equations, this method works by substituting one $y$-value with the other.
Given equations are,
\[x - 2y = 0\] and \[2x - 5y = - 4\],
Now first we have to solve one equation to one of its variable,
Here second equation is in variable $y$,
So we can now substitute the second equation in the first equation, we get
$x - 2y = 0$,
Simplifying the equation we get,
\[ \Rightarrow x = 2y\],
Now substitute the value of $x$ in the second equation i.e., \[2x - 5y = - 4\] we get,
$ \Rightarrow 2\left( {2y} \right) - 5y = - 4$,
Now simplifying we get,
\[ \Rightarrow 4y - 5y = - 4\],
Now simplifying we get,
\[ \Rightarrow -y = -4\],
Now removing the negative sign on both sides we get,
\[ \Rightarrow y = 4\],
Now substituting the value of $y$ in the first equation, we get,
$x - 2y = 0$,
Now we know that $y = 4$, now substituting we get,
$ \Rightarrow x - 2\left( 4 \right) = 0$,
Now simplifying we get,
$ \Rightarrow x - 8 = 0$,
Now add 8 on both sides we get,
$ \Rightarrow x - 8 + 8 = 0 + 8$,
Now simplifying we get,
\[ \Rightarrow x = 8\].
The value of $x$ and $y$ are, $x = 8$ and $y = 4$.

$\therefore $ When the given equations \[x - 2y = 0\] and \[2x - 5y = - 4\] are solved using substitution method, we get the value of $x$ and $y$ as, $x = 8$ and $y = 4$.

Note:
The substitution method is easy to and it works because we have equality in the objects we are substituting for any given equation. If A=B, then we would be able to use B whenever we could use A. So, when we have an equation we are free to do operations to both sides of the equation. This method is better because it makes solving equations much easier, also depending on the equation, this method involves less work and calculation. This method is the most useful system of two equations to solve two unknowns.