Question

solve the system with the addition method:4x-3y=7-20×+15y=-35Enter your answer as intergers or as reduced fraction(s) in the form A/B. If there is no solution, type "DNE" in each blank. If there are an infinite number of solutions, specify their form in the blanks in terms of x (eg. (x,2x-3)).

Answer 1

To solve the given system, first, we multiply the first equation by 5

`\begin{cases}20x-15y=35 \\ -20x+15y=-35\end{cases}`

Then, we combine the equations

`\begin{gathered} 20x-20x+15y-15y=35-35 \\ 0=0 \end{gathered}`

Hence, the system has infinitely many solutions.