The first point is (-2,2.5)
The second point is (0,2)
Step-by-step explanation:
Step 1 :
Given equation is 3x + 12y = 24
The points are
(-2,y) and (x,2)
Step 2 :
Let us take the point (-2,y)
Here x = -2 and y = y
Substituting this in the given equation we have,
3 (-2) + 12 y = 24
-6 + 12 y = 24
12 y = 24 + 6 = 30
y = 2.5
Hence the first point is (-2,2.5)
Step 3 :
The second point is (x,2)
Here x = x and y = 2
Substituting this in the given equation we have
2 x + 12 (2) = 24
2 x + 24 = 24
2 x = 24 - 24 = 0
x = 0
Hence the second point is (0,2)
Step 4 :
Answer :
The first point is (-2,2.5)
The second point is (0,2)
Answer:
0,0
Step-by-step explanation:
The function set is empty
21/9 + 74/9 = (21 + 74)/9 = 95/9 = 10 5/9
1500 divided by 60 (because 60 is 60 minutes in a hour) equals 25
so there is 25 hours in 1,500 minutes
Answer:
- The system has infinitely many solutions when a = 3/4 and b = 1/2
<h3>Given </h3>
System of linear equations
<h3>To find </h3>
- Values of a and b that leads to infinitely many solutions
<h3>Solution</h3>
The linear system of equations has infinitely many solutions when lines overlap, so both have same slope and y-intercept.
We can solve it in two different ways
1. Note that when the first equation is multiplied by 4, it has same value of constant as the second equation, which is 64.
- 4ax + 4by = 64
- 3x + 2y = 64
When compared it gives us:
- 4a = 3 ⇒ a = 3/4
- 4b = 2 ⇒ b = 2/4 = 1/2
2. Convert both equations from standard to slope-intercept form and compare:
- ax + by = 16
- by = -ax + 16
- y = - (a/b)x + 16/b
- 3x + 2y = 64
- 2y = - 3x + 64
- y = - (3/2)x + 32
Work out values of a and b:
- 16/b = 32 ⇒ b = 16/32 ⇒ b = 1/2
- - (a/b) = - 3/2 ⇒ a/b = 3/2 ⇒ a = 3b/2 ⇒ a = 3(1/2)/2 ⇒ a = 3/4