Question

How do you solve the system of equations $-7x-y=12$ and $-7x+3y=20$?

Answer 1

Hint: We will solve this set of equations using substitution method. We will take an equation, that is, $-7x-y=12$ and write the expression in terms of $$y$$.We will substitute this expression in terms of $$y$$ in the second equation which is, $-7x+3y=20$ solving which we will get the value of $$x$$. We will substitute the value of $$x$$, in the equation which we wrote in terms of $$y$$ and we get the value of $$y$$ on solving.

Complete step by step solution:
According to the given question, we have been given a set of two equations having two variables and we have to solve for $$x$$ and $$y$$. And we will be using the substitution method to solve this system of equations.
We will first take the equation $-7x-y=12$ and write it in terms of $$y$$, we have,
$$-7x-y=12$$
$$\Rightarrow y=-7x-12$$----(1)
Now, we have the expression in terms of $$y$$, substituting in the equation $-7x+3y=20$,
We get,
$$-7x+3y=20$$
$$\Rightarrow -7x+3(-7x-12)=20$$
Opening the parenthesis, we get,
$$\Rightarrow -7x+3(-7x)-3(12)=20$$
Multiplying the terms, we get,
$$\Rightarrow -7x-21x-36=20$$
Separating $$x$$ terms and the constants, we have,
$$\Rightarrow -7x-21x=20+36$$
Solving further we get,
$$\Rightarrow -28x=56$$
$$\Rightarrow -x=2$$
$$\Rightarrow x=-2$$
Substituting this value of $$x=-2$$ in equation (1), we get,
$$y=-7x-12$$
$$\Rightarrow y=-7(-2)-12$$
Solving, we have,
$$\Rightarrow y=2$$

Therefore, $$x=-2\mathrm{\&}y=2$$

Note: The substitution method used in the above method is a good method and prevents mixing the calculation for both the variables. This is because we are carrying out the calculation for each variable separately. But if the calculation in one step is done wrong then it will affect the whole answer. So, calculations need to be carried out carefully.