Question

Solve the system of equations.

3x = ­-31 + 2y
5x + 6y = 23

a. x = ­-5, y = 8
b. x = ­- 29, y = ­- 28
c.no solution
d.infinite solutions

Answer 1

a. x = -5, y = 8

Explanation:

`\left\{\begin{array}{ccc}3x=-31+2y&\text{subtract}\ 2y\ \text{from both sides}\\5x+6y=23\end{array}\right\\\\\left\{\begin{array}{ccc}3x-2y=-31&\text{multiply both sides by 3}\\5x+6y=23\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}9x-6y=-93\\5x+6y=23\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad14x=-70\qquad\text{divide both sides by 14}\\.\qquad x=-5\\\\\text{Put it to the second equation:}\\\\5(-5)+6y=23\\-25+6y=23\qquad\text{add 25 to both sides}\\6y=48\qquad\text{divide both sides by 6}\\y=8`