A signle system of linear equations has infinitely many solutions.
Two identical systems of linear equations have infinitely many solutions.
Two systems of linear equations has just one solution.
Two systems of <em>parallel</em> linear equations will has no solutions.
We have two systems of linear equations.
Let's see if they are parallel.
Parallel lines have the same slope.
We'll see if they do by converting to slope-intercept form.
(this will also let us know if they are identical)
1st Eqn.
3x - 9y = 0
Keep y on the left, x and the constant on the right...
-9y = -3x + 0
Divide by the y coefficient.
y = 1/3x + 0
2nd Eqn.
-x + 3y = -3
Keep y on the left, x and the constant on the right...
3y = x - 3
Divide by the y coefficient.
y = 1/3x - 3
As you can see, the two equations have the same slope! (1/3)
Because of this, they are parallel.
And they are not identical because the y-intercepts are different.
There are no solutions to this system of equations.
Answer: y=1/4x-3/4
Step-by-step explanation:
We have our equation of a line formula y=mx+b
Then we substitute the given and get y=1/4x-3/4
You know the first terms of the factors must be 7 & 1, since those are the only factors of 7.
So you write:
Both the second and third term are positive, so x & y are both positive.
From there, all you can really do is plug in all factors of 36 as x or y until you find that the second term adds up to 67.
And you find the only one that works is:
Answer:
3 milhas
Step-by-step explanation:
Answer:
Step-by-step explanation:
let x represent the number of minutes of call made.
Let y represent the cost for x minutes of call.
If we plot y on the vertical axis and x on the horizontal axis, a straight line would be formed. The slope of the straight line would be
Slope, m = (10.86 - 5.91)/(10 - 5)
m = 4.95/5 = 0.99
The equation of the straight line can be represented in the slope-intercept form, y = mx + c
Where
c = intercept
m = slope
To determine the intercept, we would substitute x = 10, y = 10.86 and m = 0.99 into y = mx + c. It becomes
10.86 = 0.99 × 10 + c = 9.9 + c
c = 10.86 - 9.9
c = 0.96
The linear function becomes
y = 0.99x + 0.96
Therefore, for $12, the number of minutes would be
12 = 0.99x + 0.96
0.99x = 12 - 0.96
0.99x = 11.04
x = 11.04/0.99
x = 11.15 minutes