Question

Solve $x - 2y = 0$;$3x + 4y = 20$.

Answer 1

Hint : First, the given equation is in the form of a linear equation because it has a degree at most one only.
This kind of linear equation is also represented as the straight line for the same reason (one degree).
The two linear equations can be solved by using several methods like the elimination method, substitution method, and some more factoring methods.
Here we use the elimination method to find the variables in the given question.

Complete step-by-step solution:
First, take the equation $x - 2y = 0$as equation ($1$) and $3x + 4y = 20$as the equation ($2$)
Now, multiple the number $2$on the equation ($1$) we get $2x - 4y = 0$
Compare the equation as in the form of elimination method,
$\underline 2x - 4y = 0 \\\ 3x + 4y = 20 \\\ \\\ 5x + 0y = 20 \\\$ (Since the variable $y$are equal and opposite signs, hence we canceled them and calculated the variable $x$and the constant value)
Now, further solving with the help of division operation we get, $5x = 20 \Rightarrow x = \dfrac{{20}}{5} \Rightarrow 4$
Substituting the value of x in any of the equation, here we take the equation ($1$)
$x - 2y = 0 \Rightarrow 4 - 2y = 0$ (Where $x = 4$)
Further solving this we get, $4 - 2y = 0 \Rightarrow 2y = 4 \Rightarrow y = 2$
Hence by the elimination method, we get the value of x and y as $x = 4,y = 2$for the given equations $x - 2y = 0$;$3x + 4y = 20$
Additional information:
We can also able to solve this problem by the substitution method.
From the equation $x - 2y = 0$can be converted to $x = 2y$and substitute this in the equation ($2$)
Thus, we get, $3x + 4y = 20 \Rightarrow 3(2y) + 4y = 20$
Further solving we get, $3(2y) + 4y = 20 \Rightarrow 10y = 20 \Rightarrow y = 2$
Again, substituting the value y in any of the equation we get $x - 2y = 0 \Rightarrow x - 4 = 0 \Rightarrow x = 4$
Hence, we get the same results as above.

Note: We are able to solve many ways, like as we solved elimination method and substitution method.
In the substitution method, we can substitute the value of one variable in terms of another equation.
We can also solve graphically with the help of x and y coordinates in the graph.
If the variables are at a two-degree equation then we will use the concept of the quadratic formula.