erica earns a rebate each month on her meals and movie tickets. she earns $3 for each movie ticket and $0.80 for each meal. last month erica purchased 15 meals and earned $18.

part a: create an equation that will determine the number of movie tickets she purchased.

part b: solve this equation justifying each step with an algebraic property of equality.

part c: how many movie tickets did erica purchase last month?

part A-

3t + .80m = 18 (t - tickets) (m - meals)

we already know m = 15 so our equation would turn into

3t + .80(15) = 18

3t + 12 = 18

part B-

3t + 12 = 18

subtract 12 from both sides

3t + 12 = 18

-12 -12

then, 3t= 6

and, we know 3 goes into 6 two times meaning t=2

part C- Erica purchased 2 movie tickets last month

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

77

step-by-step explanation: