Question

Solve the following systems of equations by​ elimination, if a solution exists.

6x+24y=30
20y-25=-5x

Answer 1

Answer: the system of inequalities has infinitely many solutions

Explanation:

`\displaystyle\\\left \{ {{6x+24y=30} \atop {20y-25=-5x}} \right.\ \ \Rightarrow\ \ \left \{ {{6x+24y=30} \atop {5x+20y-25=0}} \right. \ \ \ \Rightarrow \ \ \ \left \{ {{6x+24y=30} \atop {5x+20y=25}} \right.`

Multiply equation (1) by 5 and equation (2) by 6:

`\displaystyle\\\left \{ {{30x+120y=150\ \ \ \ \ (3)} \atop {30x+120y=150\ \ \ \ \ (4)}} \right. \\`

Equation (3) equals equation (4)

Hence, the system of inequalities has infinitely many solutions