Question

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

$\left\{\begin{array}{l}4x+3y=2\\ 20x+15y=10\end{array}\right.$

Short answer

The given system has infinitely many solutions.

Step-by-step solution

Step 1. Given Information 

The given linear equations are :

$\left\{\begin{array}{l}4x+3y=2\\ 20x+15y=10\end{array}\right.$

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$-5$,

localid="1644751669758" $$\begin{gathered} -5\left(4x+3y=2\right) \\ -20x-15y=-10 \end{gathered}$$

now, the equations are,

$$\begin{gathered} -20x-15y=-10 \\ 20x+15y=10 \end{gathered}$$

now simply add the equations

$-20x-15y=-1020x+15y=100=0$

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