Question

How do you solve the systems \[3x-6y=3\] and \[7x-5y=-11\]?

Answer 1

Hint: In this problem, we have to solve the given system of equations to find the value of x and y. We can add/subtract the given two systems of equations to get anyone of the x or y values and we can substitute in one of the equations to get the other value. We can add/subtract the equations by elimination method by multiplying a number to the equation in order to cancel the similar terms.

Complete step-by-step solution:
We know that the given system of equations to be solved are,
\[3x-6y=3\] ……… (1)
\[7x-5y=-11\] …….. (2)
We can now subtract the equation by elimination method.
We should know that to solve by elimination method, we should have similar terms to be cancelled, so we can multiply both equations with numbers to get similar terms.
We can now multiply 7 to the equation (1), we get
\[\Rightarrow 21x-42y=21\]
\[\Rightarrow 21x-42y-21=0\]…… (3)
 We can now multiply 3 to the equation (2), we get
\[\Rightarrow 21x-15y=-33\]
\[\Rightarrow 21x-15y+33=0\]…… (4)
Now we can subtract the above equations (3) and (4), we get
\[\begin{align}
  & \Rightarrow 21x-42y-21-\left( 21x-15y+33 \right)=0 \\
 & \Rightarrow 21x-42y-21-21x+15y-33=0 \\
\end{align}\]
Now we can cancel similar terms and simplify, we get
\[\begin{align}
  & \Rightarrow -42y+15y-21-33=0 \\
 & \Rightarrow -27y-54=0 \\
 & \Rightarrow y=-\frac{54}{27} \\
 & \Rightarrow y=-2 \\
\end{align}\]
Therefore, the value of y is -2.
Now we can substitute the y value in equation (1), we get
\[\begin{align}
  & \Rightarrow 3x-6\left( -2 \right)=3 \\
 & \Rightarrow 3x+12=3 \\
 & \Rightarrow 3x=-9 \\
 & \Rightarrow x=-3 \\
\end{align}\]
Therefore, the value of x = -3 and y = -2.

Note: Students make mistakes while multiplying the correct number to the equations for the similar terms to be cancelled. We can also directly find the value by substituting the one equation into the other. We can add/subtract the equations by elimination method by multiplying numbers to the equation in order to cancel the similar terms.