Question

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

Answer 1

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

& \Rightarrow -2x-y-\left( -2x-9y \right)=11-3 \\\ & \Rightarrow 8y=8 \\\ \end{aligned}$$ Dividing both sides of the above equation by 8 and canceling out the common factors, we get $$\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{aligned} & \Rightarrow -2x-1=11 \\\ & \Rightarrow -2x=11+1=12 \\\ & \Rightarrow x=-6 \\\ \end{aligned}$$ **Hence, the solution values for the system of equations are $$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$$