Answer:
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Answer:
Mason has
- 16 20¢ stamps;
- 25 3¢ stamps;
- 40 49¢ stamps.
Step-by-step explanation:
Let x be the number of 20¢ stamps, then the number of 3¢ stamps is x + 9.
Mason has 56 total 49¢ and 20¢ stamps, then the number of 49¢ stamps is 56 - x.
Amounts:
- in 49¢:
cents;
- in 20¢:
cents;
- in 3¢:
cents.
Total amount:
- $23.55.
Hence,
Mason has
- 16 20¢ stamps;
- 25 3¢ stamps;
- 40 49¢ stamps.
Answer:
Infinite solutions
Step-by-step explanation:
To determine the number of solutions a system has, you need its slope. If the slopes are the same, check if the equations are equivalent or not.
To find the slope, rearrange the equation to isolate "y", which makes it slope-intercept form y = mx + b.
"x" and "y" represent points on the line.
"m" represents the slope, which is how steep a line is.
"b" represents the y-intercept (where the graph hits the y-axis).
Isolate "y" in both equations:
x + 3y = 0
3y = -x Subtract 'x' from both sides
y = -x/3 Divide both sides by 3.
y =
The slope is -1/3.
9y = -3x
y = -3x/9 Divide both sides by 9
y = Reduce the fraction to lowest terms
y =
The slope is -1/3, but the two equations are the same.
Since the equations are the same, or <u>equivalent</u>, the two lines are always touching. The solution of a system means where two lines intersect, or meet. Therefore, <u>there are infinite solutions</u>.