A system of linear equations in two variables can have _____ solutions

2 answers:

8 0

If the lines are parallel (have the same slope but different intercepts) . . .
   no solution, because they never cross.

If the lines have different slopes . . .
   one solution, because they have exactly one common point.

If the lines have the same slope and the same intercept . . .
   infinitely many solutions, because every point on one line is also a point on
   the other line, one lays right on top of the other, and when you look at them on
   the graph, it looks like only one line.

madreJ [45]2 years ago

5 0

One solution
or no solution
or an infinite number of solutions

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Alexus [3.1K]

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3 years ago

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A painter charges an initial fee of $50 and $30 for each hour of labor. Write a linear function to determine the total cost. How

il63 [147K]

The initial fee of $50 is essentially the y intercept because this is the value when x = 0 (x is the number of labor-hours). So b = 50.

The slope is m = 30 because each increase of 1 hour leads to the cost bumping up by 30 dollars. In other words, slope = rise/run = (change in cost)/(change in hours) = 30/1

So we plug m = 30 and b = 50 into the y = mx+b formula to get y = 30x+50

Replace y with f(x) to get f(x) = 30x+50

The linear function for the cost is f(x) = 30x+50

Note: Some books may use other letters (instead of x and f(x)), but the idea is still the same

Once you know the cost function, you replace x with 4.5 to find the amount it will cost to have a painter work for 4.5 hours.

f(x) = 30x+50
f(4.5) = 30*4.5+50
f(4.5) = 135+50
f(4.5) = 185

It will cost 185 dollars to have the painter work for 4.5 hours

7 0

3 years ago

1. Solve the equation.<br>4(x + 5) = 24<br><br>

bixtya [17]

Answer:

x=1

Step-by-step explanation:

4(x+5)= 24

4x+20=24

-20 -20

____________

4x = 4