Answer:
Each fern costs $11 and each lilly costs $7
Step-by-step explanation:
Let x be ferns and y be lilies
[tex]8x+15y=193\\3x+12y=117[/tex]
Let's solve for 3 in the second equation.
[tex]3x+12y=117\\3x=117-12y\\x=\frac{117-12y}{3}[/tex]
Now replace x in the first equation.
[tex]8x+15y=193\\8(\frac{117-12y}{3})+15y=193\\ \frac{936-96y}{3}+15y=193[/tex]
Break down the fraction.
[tex]\frac{936}{3}-\frac{96}{3}y+15y=193[/tex]
[tex]312-\frac{96}{3}y+15y=193[/tex]
Subtract 312
[tex]-\frac{96}{3}y+15y=193-312[/tex]
Combine like terms;
[tex]\frac{-96+3*15}{3}y=-119[/tex]
Solve;
[tex]\frac{-96+45}{3}y=-119[/tex]
[tex]\frac{-51}{3}y=-119[/tex]
[tex]-17y=-119[/tex]
Divide by -17
[tex]y=\frac{-119}{-17}\\ y=7[/tex]
Now replace y in any of the equations to find x.
[tex]3x+12y=117\\3x+12(7)=117\\3x+84=117\\3x=117-84\\3x=33\\x=\frac{33}{3}\\ x=11[/tex]
