Question

How do you solve $3r-5s=-35$ and $2r-5s=-30$?

Answer 1

Hint: There are equations in two variables and we have to solve the given equations. We will use the elimination method to solve the given equations. For this we subtract the second equation from the first equation and then substitute the obtained value of the variable in one of the equations to get the value of another variable.

Complete step-by-step solution:
We have been given equations $3r-5s=-35$ and $2r-5s=-30$.
We have to solve the given equations.
We have
$3r-5s=-35..........(i)$
$2r-5s=-30...........(ii)$
We will use elimination methods to solve the given equations. First we will subtract the equation (ii) from equation (i). Then we will get
$\begin{align}
  & 3r-5s=-35 \\
 & -\underline{\left( 2r-5s=-30 \right)} \\
 & r=-5 \\
\end{align}$
So by solving the equations we get the value $\Rightarrow r=-5$
Now, substituting the value in equation (i) we will get
$\Rightarrow 3\left( -5 \right)-5s=-35$
Now, simplifying the above obtained equation we will get
$\Rightarrow -15-5s=-35$
Now, shifting the constant term to the right side we will get
$\Rightarrow -5s=-35+15$
Now, simplifying the above obtained equation we will get
$\Rightarrow -5s=-20$
Now, dividing the above obtained equation by 5 we will get
\[\Rightarrow \dfrac{-5s}{5}=-\dfrac{20}{5}\]
Now, simplifying the above obtained equation we will get
$\begin{align}
  & \Rightarrow -s=-4 \\
 & \Rightarrow s=4 \\
\end{align}$
Hence on solving the given equations we get the values of r and s as $-5$ and 4 respectively.

Note: Alternatively one can use other methods like substitution method, graphing method to solve the given equations. If the coefficients of the variables are not equal then to eliminate a variable we need to divide or multiply the equation by any suitable number.