Question

How do you solve $3x-y=4$ and $2x+y=6$?

Answer 1

Hint: We will solve this question using the method of elimination. We can see that y-terms of both the equations are similar in magnitude but opposite in signs. So we will add the two equations and the y-terms will get cancelled. We will have the terms expressed in terms of x and solving further we will get the value of x. substituting this value of x in any of the equations given we will get the value of y as well.

Complete step by step answer:
According to the question given, we have to solve for $x$ and $y$, for the given set of equations using elimination method.
Elimination method, from the name itself we can figure out that elimination is involved that is while solving the equations one of the variable is eliminated so that the value of the other variable can be found. And then substituting that value in any of the equations we have the values of both the variables.
We have,
$3x-y=4$----(1)
 $2x+y=6$-----(2)
We can see that the y-terms in both the equations have same magnitude and opposite signs, so we will add both the equations so that y-terms get cancelled and we can find the value of $x$.
We have,
   $3x-y=4$
$\underline{+(2x+y=6)}$
     $5x=10$----(3)
We get the value of $x$ as,
$\Rightarrow x=2$
Putting this value of $x$ in equation (2), we get,
$2x+y=6$
$\Rightarrow 2(2)+y=6$
$\Rightarrow 4+y=6$
Subtracting 4 on both sides we get,
$\Rightarrow 4+y-4=6-4$
$\Rightarrow y=6-4$
$\Rightarrow y=2$

Therefore, $x=2\And y=2$.

Note: The above solution was calculated using elimination method, but we can also solve this question using substitution method or cross multiplication method. Elimination method reduces the possibilities of making mistakes by eliminating one variable and we solve one variable at a time. Also, to check if the values obtained are correct or not, substitute the values in any of the two given equations.