Question

How do you solve $3x+y=7$ and $3x-y=5$?

Answer 1

Hint: We will be solving this set of equations using elimination method. The equations given to us have the same y-component so we do not have to make any additional effort to them. We will add the two equations so that the y-terms will get cancelled. We now have equations in terms of $x$ and solve to get the value of $x$. We will then substitute this value of $x$ in any of the two equations above and solve to get the value of $y$.

Complete step by step answer:
According to the given question, we have been given two equations with two variables namely $x$ and $y$, whose values we have to find.
To solve for $x$ and $y$, we will use elimination method, we have,
$3x+y=7$-----(1)
$3x-y=5$-----(2)
Adding equations (1) and (2), we get,
   $3x+y=7$
$\underline{+(3x-y=5)}$
   $6x=12$----(3)
We get the value of $x$ as,
$\Rightarrow x=2$
Substituting this value of $x=2$ in equation (1), we get,
$3x+y=7$
$\Rightarrow 3(2)+y=7$
We will proceed on to find the value of $y$, we have,
$\Rightarrow 6+y=7$
Subtracting 6 on both the sides of the equality, we have,
$\Rightarrow 6+y-6=7-6$
$\Rightarrow y=1$

Therefore, $x=2$ and $y=1$.

Note: The above question can also be solved using the substitution method, which is as follows,
We have the equation as,
$3x+y=7$-----(1)
$3x-y=5$-----(2)
We will now write equation (2) in terms of $y$, we get,.
$3x-y=5$
$\Rightarrow y=3x-5$----(3)
Substituting equation (3) in equation (1), we get,
$3x+y=7$
$\Rightarrow 3x+(3x-5)=7$
Solving this expression gives us the value of $x$, we have,
$\Rightarrow 3x+3x-5=7$
Separating the x-terms and the constants, we have,
$\Rightarrow 3x+3x=7+5$
$\Rightarrow 6x=12$
$\Rightarrow x=2$
We have the value of $x$, we will now substitute this value of $x$ in the equation (3),
$y=3x-5$
$\Rightarrow y=3(2)-5$
$\Rightarrow y=6-5$
$\Rightarrow y=1$
Therefore, $x=2$ and $y=1$.