Question

How do you solve the system $7x+3y=25$ and $-2x-y=-8$?

Answer 1

Hint: There are several methods to solve the system of equations having two variables. For this problem we will go with the method of multiplication. In this method we will consider coefficients of either $x$ or $y$ and calculate the LCM of the coefficients. Now we will multiply both the equations with respective constants to get a unique coefficient for the variable either $x$ or $y$. Now we will add or subtract the one equation from another equation to obtain an equation which is in a single variable. From this equation we can find the value of one variable and from this value and by using any one of the given equations we can find the second variable.

Complete step by step answer:
Given equations, $7x+3y=25$ and $-2x-y=-8$.
Coefficients of $x$ are $7$, $-2$.
Coefficients of $y$ are $3$, $-1$.
From our easiness consider the coefficients of $y$.
The LCM of $3$, $1$ is $3$.
Multiplying the equation $-2x-y=-8$ with $3$, then we will get
$\begin{align}
  & 3\left( -2x-y \right)=3\times -8 \\
 & -6x-3y=-24 \\
\end{align}$
Adding the equation $7x+3y=25$ to the above equation, then we will get
$-6x-3y+7x+3y=-24+25$
Simplifying the above equation, then we will get
$x=1$
Substituting the value of $x$ in $-2x-y=-8$, then we will get
$\begin{align}
  & -2\left( 1 \right)-y=-8 \\
 & \Rightarrow y=8-2 \\
 & \Rightarrow y=6 \\
\end{align}$

Hence the solution of the system $7x+3y=25$ and $-2x-y=-8$ is $x=1$, $y=6$.

Note: We can check whether the obtained result is correct or wrong by substituting the obtained result in the both of the given equations. If the obtained results satisfy the both the given equation, then our solution is correct. If any one of the equations is not satisfied by the obtained solution, then our solution is not correct.