Your family goes to a restaurant for dinner. there are 6 people in your family. some order the chicken dinner for $14.80 and some order the steak dinner for $17. if the total bill was $91, how many people ordered each type of dinner?

This is a linear system
you can graph both lines and see where the intercept or make an equation for both and then solve it for a point that can solve both equations. I'm going to use the subsitution method

x is steak
y is chicken

x+y=6 <-- for the amount of steaks + amount of chicken should be equal to 6 meals, 1 for each person
17x+14.80y=91 <--$17 for each steak + 14.80 for each chicken should be $91

x+y=6
get one of the 2 variables alone on one side. I'm doing it for x
x=-y+6
since thats what y is in terms of x, subsitute that for x in the other equation
17(-y+6)+14.80y=91
distribute the 17
-17y+102+14.80y=91
combine like terms
-2.2y+102=91
subtract 102
-2.2y=-11
divide by 102 now you have y alone
y=5
because before you got y in terms of x you know that x is equivalent to negative y + 6. now we have y (5) so subsitute that in to get x
x=-(5)+6
simplify
x=1
now you have x=1 and y=5. you know y is chicken and x is steak so theres your answer! (1 person got steak 5 people got chicken)
you can plug in x and y in both quations and make sure its right
x+y=6 --> 1+5=6 --> 6=6
that eqaution's true
17x+14.80y=91 --> 17(1)+14.80(5)=91 --> 17+74=91 --> 91=91
both equations are true so your answer is right

hope that hhelps you :)

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