Question

5x - 2y = 6 x = 5 - y solve the system of equations by substitution. a. (16/7, 19/7) b. (-4/3, 19/3) c. no solution d. coincident

Answer 1

`\large\boxed{a.\ \left((16)/(7),\ (19)/(7)\right)}`

Explanation:

`\left\{\begin{array}{ccc}5x-2y=6&(1)\\x=5-y&(2)\end{array}\right\\\\\text{Put (2) to (1):}\\\\5(5-y)-2y=6\qquad\text{use the distributive property}\\(5)(5)+(5)(-y)-2y=6\\25-5y-2y=6\qquad\text{subtract 25 from both sides}\\-7y=-19\qquad\text{divide both sides by (-7)}\\y=(19)/(7)\\\\\text{Put it to (2):}\\\\x=5-(19)/(7)\\\\x=(35)/(7)-(19)/(7)\\\\x=(16)/(7)`