Question

Determine the equivalent system for the given system of equations:

5x − 3y = 6
x + y = 2

Answer 1

Your answer would be A.) 5x − 3y = 6 and 6x − 2y = 8

Answer 2

x = 1.5 and y = 0.5 → (1.5, 0.5)

Explanation:

`\left\{\begin{array}{ccc}5x-3y=6\\x+y=2&\text{multiply both sides by 3}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}5x-3y=6\\3x+3y=6\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad8x=12\qquad\text{divide both sides by 8}\\.\qquad x=1.5\\\\\text{put the value of x to the second equation:}\\\\1.5+y=2\qquad\text{subtract 1.5  from both sides}\\y=0.5`