Answer:42x5=210/14=15
Step-by-step explanation:Each student would get 15 pencils
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
Answer:
The solution is: x = -1, and y = 8/3
Step-by-step explanation:
Notice that the system of equations can be easily solved via the "elimination" method, by subtracting term by term one equation from the other. Doing such will remove completely the term in "y" (since the terms in "y" are exactly equal in both equations), and leave only an equation containing "x", for which the value can be solved:
Now we use this x-value in either equation to solve for y:
Answer:3.162e+7
Step-by-step explanation:in 1 hour it is
Answer:
y + 5 = 2(x - 3)
General Formulas and Concepts:
<u>Algebra I</u>
Point-Slope Form: y - y₁ = m(x - x₁)
- x₁ - x coordinate
- y₁ - y coordinate
- m - slope
Step-by-step explanation:
<u>Step 1: Define</u>
Point (3, -5)
Slope <em>m</em> = 2
<u>Step 2: Write equation</u>
<em>Substitute in variables into the general form.</em>
y + 5 = 2(x - 3)
