Question

Solve the following system of linear equation
\[\begin{array}{l}
x - 2y = 0\\
3x + 4y = 20
\end{array}\]

Answer 1

Hint: Observe the two equations closely and try to solve them by either elimination or substitution method as it can be done easily by any one of them. Choose the method with which you want to solve and proceed accordingly.

Complete Step by Step solution:
Let's Name the equations first
\[\begin{array}{l}
x - 2y = 0..........................................................(i)\\
3x + 4y = 20.......................................................(ii)
\end{array}\]
Now let's try to solve it by substitution method
So from equation (i) it is clear that \[x = 2y\]
Now let's try to put this value in equation (ii) and see what we are getting.
\[\begin{array}{l}
 \Rightarrow 3x + 4y = 20\\
 \Rightarrow 3 \times 2y + 4y = 20\\
 \Rightarrow 6y + 4y = 20\\
 \Rightarrow 10y = 20\\
 \Rightarrow y = 2
\end{array}\]
So by putting \[x = 2y\] we are getting \[y = 2\]
Now let's put this value of y in the modified form of equation (i)
\[\begin{array}{l}
\therefore x = 2y\\
 \Rightarrow x = 2 \times 2\\
 \Rightarrow x = 4
\end{array}\]
So we are getting \[x = 4\& y = 2\]

Note: This question can also be solved by using elimination method and by the rule of elimination method we know that either one of the two coefficients in both the equation must be the same(signs can be different), but in this case none of them satisfies the rule so we have to multiply equation (i) with 2 which will give us \[2x - 4y = 0\] now the y-coefficient is same in both the equation(signs are different) so in this case we can just add both the equation so we will be left with only one variable i.e., x by solving the resulting equation we will get the value of x and after that just put the value of x in equation (i) to get the value of y. The answer remains the same regardless of what method we follow i.e., \[x = 4\& y = 2\]