Question

How do you solve the system using the elimination method for \[4x+6y=24\] and \[4x-y=10\]?

Answer 1

Hint: For the given problem we are given to solve the given equations in the elimination process. For that we have to eliminate any of the variables using operations for solving the above problem we have to subtract the first equation from the second equation for solving these problems.

Complete step by step solution:
For the given problem we are given to solve the given two equations \[4x+6y=24\] and \[4x-y=10\] by the elimination process.
Elimination process is the process in which we have to eliminate any variable in the equation by adding or subtracting or by doing any operations.
Let us consider the two equations as equation (1) and equation (2) respectively.
\[4x+6y=24.............\left( 1 \right)\]
\[4x-y=10..............\left( 2 \right)\]
Now by observing the equation (1) and equation (2), we can see that 4x is the common term in both equation (1) and equation (2). So, let us subtract the both equations to get the equation in one variable.
By subtracting equation (1) from equation (2), we get
\[\Rightarrow 4x-y-4x-6y=10-24\]
By simplifying the equation, we get
\[\Rightarrow -7y=-14\]
Now by dividing the above equation with -7, we get
\[\Rightarrow y=2\]
Let us consider the above equation as equation (3), we get
\[\Rightarrow y=2...................\left( 3 \right)\]
Let us substitute equation (3) in the equation (2), we get
\[\Rightarrow 4x-2=10\]
By adding with 2 on both sides of the above equation, we get
\[\Rightarrow x=3\]
Let us consider the above equation as equation (4), we get
\[\Rightarrow x=3................\left( 4 \right)\]
Therefore, equation (3) and equation (4) are the solutions for the given problem.

Note: We should compare the two equations before doing any operations for eliminating the variable. We should be aware of solving this type of problems. Elimination process is the easiest process when compared with the substitution method.