y = -x + 5
5x + 2y = 14
5x + 2(-x + 5) = 14
5x + 2(-x) + 2(5) = 14
5x - 2x + 10 = 14
3x + 10 = 14
- 10 - 10
3x = 4
3 3
x = 1¹/₃
y = -x + 5
y = -1¹/₃ + 5
y = 3²/₃
(x, y) = (-1¹/₂, 3²/₃)
Answer:
-3, -2.1, -2, 0
Step-by-step explanation:
Least to greatest
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(a) Answer: One solution.
Explanation: two lines that have same slope with opposite sign will necessarily cross each other at a single point, as one is "pointing uphill" and the other "downhill."
(b) Answer: Infinitely many solutions.
Explanation:
2x + 3y = 5.5
4x + 6y = 11 | divide by 2
-->
2x + 3y = 5.5
2x + 3y = 5.5
--> equations are identical.
2x + 3y = 2x + 3y
so any (x,y) will satisfy this equation. This means infinitely many solutions.
(c) Answer: One solution
Explanation:
Continuing the two lines it becomes obvious they will cross at one point (the solution)
(d) Answer: No solution
Explanation: If the two lines are parallel, they will never cross (by definition of "parallel"). Therefore there will be no solution to the corresponding linear system.
2^10 = 1024 possible ways to answer the test
0.10d + 0.25q = 3.55
q = d + 3
0.10d + 0.25(d + 3) = 3.55
0.10d + 0.25d + 0.75 = 3.55
0.10d + 0.25d = 3.55 - 0.75
0.35d = 2.80
d = 2.80/0.35
d = 8.....8 dimes
q = d + 3
q = 8 + 3
q = 11 <=== 11 quarters