Question

How do you solve $y\, = \,4x$ and $x\, + \,y\, = \,5?$

Answer 1

We take either $x\,or\,y$ in terms of each other and substitute the value in the second equation. Solving the equation, we get the values of both $x\,and\,y$.

Complete step by step answer: Here it is given that $y\, = \,4x$ so substituting this value of y which is in terms of x in the other equation that is $x\, + \,y\, = \,5$ .
So, we can write the equation $x\, + \,y\, = \,5$ in terms of $x\,$ as shown below:
$x\, + \,4x\, = \,5$
This can be further simplified by adding the $x\,$terms, we can have
$\,5x\, = \,5$
On dividing by $5$ on both sides of the equation, we get
$\,\dfrac{{5x}}{5}\, = \,\dfrac{5}{5}$
We just cancelled the same terms from the numerator and the denominators and after
Simplifying it we get
$\,x\, = \,1$
Now, as we get the value of $x\,$, we can find the value of $y$
Since, $y\, = \,4x$
Substituting the value of $x\,$ to find the value of $y$, we can get
$y\, = \,4 \times \,1$
Therefore, $1\,and\,\,4$
Hence, the values of $x\,and\,y$ are $1\,\,and\,\,4$ respectively.

Note:
We can solve the question using other methods as well. We can start with second equation, find $x\,$ in terms of $y$ and then substitute the value of $y$ to get the value of $x\,$ as shown below:
$x\, + \,y\, = \,5$
Transposing $y$ on other side of the equation and finding $x\,$ in terms of $y$
Hence we get
$x\, = \,5\, - \,y$
No substituting this value of $x\,$ in the equation$y\, = \,4x$, we get
$y\, = \,4 \times (5\, - \,y)$
Solving this equation, we get
$y\, = \,20 - 4y$
Transposing $4y$ on the left side we get
$y\, + 4y = \,20$
On solving this linear equation, we get the value of $y$.
$5y = \,20$
We are just dividing, $y = \dfrac{{20}}{5}$
Hence we get,
$y\, = \,4$
Now, putting this value of $y$ in the equation $y\, = \,4x$ we get,
$x\, = \,\dfrac{y}{4}$
Therefore $x\, = \,\dfrac{4}{4}$
$x\, = \,1$
Therefore, we get the solution as $(x,y)\, = \,(1,4)$