Question

SOLVING SYSTEMS OF EQUATIONS BY SUBSTITUTION. 1. 2x+3y=1 -3x+y=15

Answer 1

$2x+3y=1 \\ -3x+y=15 \\ \\ \hbox{from the 2nd equation:} \\ -3x+y=15 \\ y=15+3x \\ \\ \hbox{substitute 15+3x for y in the 1st equation:} \\ 2x+3(15+3x)=1 \\ 2x+45+9x=1 \\ 9x+2x=1-45 \\ 11x=-44 \\ x=-4 \\ \\ \hbox{solve one of the equations for y}: \\ 2x+3y=1 \\ 2 \cdot (-4) + 3y=1 \\ -8+3y=1 \\ 3y=1+8 \\ 3y=9 \\ y=3 \\ \\ \hbox{the answer:} \\ x=-4 \\ y=3$