Answer:
7)Bagel costs $3.5 and muffin cost $1.25
8) Ticket is $9 while snacks are $2
9) Correct because left hand side is zero
10) Correct because they both have same slope and same y-intercept
Step-by-step explanation:
7) Let bagel be x and muffin be y.
Thus;
For Aaron;
x + 3y = 7.25 - - - (1)
For bee;
x + 2y = 6 - - - (2)
Subtract eq 2 from eq 1 to get;
y = 1.25
Put 1.25 for y in eq 2;
x + 2(1.25) = 6
x + 2.5 = 6
x = 6 - 2.5
x = 3.5
Bagel costs $3.5 and muffin cost $1.25
8) Let movie ticket be x and snacks be y.
Thus;
2x + 3y = 24 - - - (1)
3x + 4y = 35 - - - (2)
Multiply eq(1) by 3 and eq(2) by 2 to get;
6x + 9y = 72 - - - (3)
6x + 8y = 70 - - - (4)
Subtract eq 4 from eq 3 to get;
y = 2
Put 2 for y in eq 3;
6x + 9(2) = 72
6x + 18 = 72
6x = 72 - 18
6x = 54
x = 54/6
x = 9
Ticket is $9 while snacks are $2
9) using elimination, subtract eq 1 from eq 2, we will see that the entire left hand side is equal to zero.
Thus, no solution exists because we can't isolate the variable to get an answer.
10) The answer is correct because for a system of 2 simultaneous equations to have infinite solutions, they both have to have the same y-intercept and also same slope.
In this case, their y-intercept which is when x is 0 is;
3(0) + y = 9
y = 9
Their slope is also the same equal to 3.
