Question

Solve the system shown below:

-x + 9y = 9
2x - 3y = 12

How many solutions are there to the system?
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1 point
One Solution
Two Solutions
No Solutions
Infinitely Many Solutions
Two lines are graphed on a coordinate plane. The equation of the first line is 2x - y = 6 and the equation of the second line is x + 2y = 10. Describe the relationship between the two lines and how you know. Do the equations represent parallel lines, perpendicular lines, coinciding lines (i.e., the same line), or intersecting lines that are not perpendicular? If the lines intersect, identify the point of intersection.
*
1 point
Coinciding Lines
Intersecting Lines at (2.8, 4.4)
Intersecting Lines at (4.4, 2.8)
Parallel Lines
Perpendicular Lines
A movie theater charges different prices for children and adults. On Friday, 10 adults and 25 children went to the movie and it cost $670. On Sunday 5 adults and 10 children went and it cost $290.

Let c = the price of a child’s ticket

Let a = the price of an adult ticket

What is the cost of each adult ticket? Enter the amount as a dollar amount. For example, if the answer is 5 dollars, type $5.00.

Answer 1

1) Solve -x + 9y = 9 and 2x - 3y = 12
x = 9y - 9; substitute: 2(9y-9) - 3y = 12 → 15y = 30 → y = 2, x = 9.
How many solutions? One Solution. (Unique solution (9, 2))

2) Lines 2x - y = 6 and x + 2y = 10
Rewrite: y = 2x - 6 (slope 2) and y = -½x + 5 (slope -1/2). Slopes multiply to -1, so the lines are perpendicular. They intersect at the solution of the system: 2x - 6 = -½x + 5 → x = 4.4, y = 2.8.
So: Perpendicular lines; intersection at (4.4, 2.8).

3) Ticket prices
10a + 25c = 670
5a + 10c = 290 → multiply by 2: 10a + 20c = 580
Subtract: 5c = 90 → c = $18.00. Then 5a + 10(18) = 290 → 5a = 110 → a = $22.00.

Answer for adult ticket: $22.00.