Answer – The solution $\mathbf{(}\mathit{x}\mathbf{,}\mathbf{ }\mathit{y}\mathbf{)}$ to the system of linear equations $\mathbf{3}\mathit{x}\mathbf{ }\mathbf{–}\mathbf{ }\mathit{y}\mathbf{ }\mathbf{=}\mathbf{ }\mathbf{–}\mathbf{12}$ and $\mathbf{3}\mathit{x}\mathbf{ }\mathbf{+}\mathbf{ }\mathit{y}\mathbf{ }\mathbf{=}\mathbf{ }\mathbf{–}\mathbf{18}$ is $\mathbf{(}\mathbf{–}\mathbf{5}\mathbf{,}\mathbf{ }\mathbf{–}\mathbf{3}\mathbf{)}$.

Explanation:

A system of linear equations is a set of two or more equations with two or more variables. It requires all equations that are a part of it to be considered while solving for the variables. 

The given system of equations includes 2 linear equations $3x – y = –12$ and $3x + y = –18$ with 2 variables x and y. 

And to solve this system of linear equations, we can employ the process of elimination. This means that we remove one of the two variables by either adding or subtracting the equations. Once we solve for one variable, we can solve for the other by substituting the first variable in either equation.

It’s useful to note that in any system of linear equations, if one of the variables has opposite coefficients, then the equations must be added. On the other hand, if a variable has the same coefficients, the equations must be subtracted from one another.

In the given linear equations, we see that y has opposite coefficients 1 and -1 and hence can easily be eliminated by adding the two equations:

$3x – y = –12$

$+ (3x + y = –18)$

$\Rightarrow 6x = –30$

$\Rightarrow x = –5$

Now that we know x, we can substitute its value in either of the two given equations to get the value of y.

Let’s substitute for x in $3x + y = –18$ to solve for y:

$3(–5) + y = –18$

$\Rightarrow –15 + y = –18$

We can now add 15 on both sides of the equation to simplify further:

$–15 + y = –18$

$+15 +15$

$\Rightarrow y = –3$

So the solution $(x,y)$ to the given system of linear equations is $(–5, –3)$.

Popular Questions