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
In explicit representation, a sequence is represented in terms of the first term while in recursive representation, a sequence is represented in terms ot the previous term.
Eg, the sequence: 2, 4, 6, 8, 10, . . .
Explicit Reprecentation An = 2 + 2(n - 1)
Recursive representation f(n) = 2 + f(n - 1)
there is no questions to answer
Answer:
x = 24/13
General Formulas and Concepts:
<u>Pre-Alg</u>
- Order of Operations: BPEMDAS
- Equality Properties
Step-by-step explanation:
<u>Step 1: Define equation</u>
18/13 = 3/4x
<u>Step 2: Solve for </u><em><u>x</u></em>
- Divide both sides by 3/4: x = 24/13
<u>Step 3: Check</u>
<em>Plug in x to verify it's a solution.</em>
- Substitute: 18/13 = 3/4(24/13)
- Multiply: 18/13 = 18/13