Question

How do you solve the system of equations$-6x-10y=20$ and $3x+5y=25$?

Answer 1

Hint: To solve the system of equations in two variables, we need to follow the steps given below in the same order:
Step 1: choose one of the equations to find the relationship between the two variables. This can be done by taking one of the variables to the other side of the equation.
Step 2: substitute this relationship in the other equation to get an equation in one variable.
Step 3: solve this equation to find the solution value of the variable.
Step 4: substitute this value in any of the equations to find the value of the other variable.

Complete step by step solution:
We are given the two equations $-6x-10y=20$ and $3x+5y=25$. We know the steps required to solve a system of equations in two variables. Let’s take the first equation $-6x-10y=20$.
Simplifying this equation, we get \[6x=-20-10y\]. Dividing both sides of the above equation, we get \[3x=-10-5y\].
Substituting this in the equation $3x+5y=25$, we get
\[\begin{align}
  & \Rightarrow -10-5y+5y=25 \\
 & \Rightarrow -10=25 \\
\end{align}\]
But this can never be true. Hence, there is no solution for y, using this we can say that there is no solution of x.

Hence, the set of equation has no solution.

Note: To solve any system of equations having two variables, we need to follow the given steps.
We can solve the above system of equation easily by using the property given below:
For a set of equations \[ax+by+c=0\And mc+ny+o=0\]. There is no solution if \[\dfrac{a}{m}=\dfrac{b}{n}\ne \dfrac{c}{o}\].