Q 60 - Intermediate Algebra

Question

In the following exercise, solve the systems of equations by elimination.

$\left\{\begin{array}{l}2x+y=3\\ 6x+3y=9\end{array}\right.$

Step-by-Step Solution

Answer

The given system has infinitely many solutions.

Step 1. Given information

The given linear equations are :

$$\begin{gathered} 2x+y=3 \\ 6x+3y=9 \end{gathered}$$

Step 2. Calculating the value of y

To calculate the value of $y$, we have to eliminate the $x$ term. For which we will do the following changes in the equation, so that $x$ term can be easily eliminated.

Multiply the first equation by $-3$

$$\begin{gathered} -3\left(2x+y=3\right) \\ -6x-3y=-9 \end{gathered}$$

 now, the equations are 

$$\begin{gathered} -6x-3y=-9 \\ 6x+3y=9 \end{gathered}$$

now simply add the equations

$-6x-3y=-9+6x+3y=90=0$

this means that the above equation is satisfied for all the values of $x$ and $y$.