Question

How do you solve this system of equations \[-2x-y=11\] and \[-2x-9y=3\]?

Answer 1

Hint: To solve this system of equations: as we can see that the coefficient of variable x in both equations is the same. We can use this to make things simple. If we subtract the first equation from the other, the x terms will get canceled out. And, we will get a linear equation in one variable. By solving this equation, we will get the solution value of the variable. Using this value, we can also find the value of x that satisfies the equation.

Complete step by step solution:
We are given the two equations \[-2x-y=11\] and \[-2x-9y=3\].
As we can see that the coefficient of x in both equations is the same, we can also solve this problem as follows
Subtracting the second equation from the first, we get
\[\begin{align}
  & \Rightarrow -2x-y-\left( -2x-9y \right)=11-3 \\
 & \Rightarrow 8y=8 \\
\end{align}\]
Dividing both sides of the above equation by 8 and canceling out the common factors, we get
\[\Rightarrow y=1\]
We get the solution value of y, to find the solution value of x, we substitute this value in the first equation, by doing this we get
\[\begin{align}
  & \Rightarrow -2x-1=11 \\
 & \Rightarrow -2x=11+1=12 \\
 & \Rightarrow x=-6 \\
\end{align}\]
Hence, the solution values for the system of equations are \[x=-6\] and \[y=1\].

Note: We can also use the standard methods to solve this set of equations as follows,
We know the steps required to solve a system of equations in two variables. Let’s take the first equation, we get
\[\Rightarrow -2x-y=11\]
Adding y to both sides of equation, we get
\[\Rightarrow -2x=11+y\]
Substituting this in the equation \[-2x-9y=3\], we get
\[\Rightarrow 11+y-9y=3\]
Simplifying the above equation, we get
\[\Rightarrow y=1\]
Substituting this value in the relationship between variables to find the value of x, we get
\[\Rightarrow -2x=11+1=12\]
Dividing both sides by \[-2\] to above equation, we get
\[\Rightarrow x=-6\]