Question

How do you solve $2x - y = 7$ and $3x + y = 8$?

Answer 1

Hint: First we take anyone’s equation, that equation is considered $y$. That $y$ equation applies to another equation. After applying we do that to simplify. Then we get a $x$ value.
After that the $x$ value substitutes the considered equation of $y$.
We use the simplify method.
After we get the $y$.
And finally we get the $x$ and $y$ values.

Complete step-by-step solution:
The given equation is,
$2x - y = 7$and $3x + y = 8$
From the first equation, we can write it as, $y = 2x - 7$
Substitute this expression for $y$ in the second equation and we get
$ \Rightarrow 3x + (2x - 7) = 8$
Separate the $x$ term, hence we get
$ \Rightarrow 3x + 2x - 7 = 8$
Now add the $x$ term, we get
$ \Rightarrow 5x - 7 = 8$
The constant change in RHS (Right Hand Side)
$ \Rightarrow 5x = 8 + 7$
Now add the constant terms, we get
$ \Rightarrow 5x = 15$
Divide by $5$ on both sides, hence we get
$ \Rightarrow \dfrac{{\not{5}x}}{{\not{5}}} = \dfrac{{15}}{5}$
$ \Rightarrow x = 3$
Now the $x$ value substitute in the equation of $y = 2x - 7$, we get
$ \Rightarrow y = 2(3) - 7$
Multiply the first term, we get
$ \Rightarrow y = 6 - 7$
Subtract, hence we get $y$ value
$ \Rightarrow y = - 1$

Hence the $x$ and $y$ value is $3$ and $ - 1$ respectively.

Note: $2x - y = 7 \to 1$
$3x + y = 8 \to 2$
Now we add equation $1$ and $2$, hence we get
\[\begin{array}{*{20}{c}}
  {2x - y = 7} \\
  {\underline {3x + y = 8} } \\
  {5x + 0 = 15}
\end{array}\]
On simplify we get,
$ \Rightarrow 5x = 15$
On dividing we get
$ \Rightarrow x = 3$
Now the $x$ value substitute in the equation of $y = 2x - 7$, we get
$ \Rightarrow y = 2(3) - 7$
Multiply the first term, we get
$ \Rightarrow y = 6 - 7$
Subtract, hence we get $y$ value
$ \Rightarrow y = - 1$
Hence the $x$ and $y$ value is $3$ and $ - 1$ respectively.