Answer:
(3, 2)
Step-by-step explanation:
Answer: the cost of each pencil is $0.5
the cost of each eraser is $0.15
Step-by-step explanation:
Let x represent the cost of one pencil.
Let y represent the cost of one eraser.
Becky spent $1.45 for 2 pencils and 3 erasers. This means that
2x + 3y = 1.45- - - - - - - - - -1
Luke spent $2.65 for 5 pencils and 1 eraser. This means that
5x + y = 2.65- - - - - - - - - -2
Multiplying equation 1 by 1 and equation 2 by 3, it becomes
2x + 3y = 1.45
15x + 3y = 7.95
Subtracting, it becomes
- 13x = - 6.5
x = - 6.5/- 13
x = 0.5
Substituting x = 0.5 into equation 2, it becomes
5 × 0.5 + y = 2.65
2.5 + y = 2.65
y = 2.65 - 2.5
y = 0.15
Answer:
D. (1, -2)
General Formulas and Concepts:
<u>Pre-Algebra</u>
- Order of Operations: BPEMDAS
- Equality Properties
<u>Algebra I</u>
- Solving systems of equations using substitution/elimination
Step-by-step explanation:
<u>Step 1: Define systems</u>
5x - 2y = 9
3x + 4y = -5
<u>Step 2: Rewrite systems</u>
10x - 4y = 18
3x + 4y = -5
<u>Step 3: Solve for </u><em><u>x</u></em>
- Add to equations together: 13x = 13
- Divide 13 on both sides: x = 1
<u>Step 4: Solve for </u><em><u>y</u></em>
- Define: 3x + 4y = -5
- Substitute in <em>x</em>: 3(1) + 4y = -5
- Multiply: 3 + 4y = -5
- Isolate <em>y </em>term: 4y = -8
- Isolate <em>y</em>: y = -2
And we have our final answer!
