KYOTE Algebraic Reasoning 3

Question 1

Solve the system: 2x + y = 7 and x − y = 2.

Accepted Answer

x = 3, y = 1

Answer

Adding the equations: 3x = 9, so x = 3; substituting gives y = 1.

Question 2

Which expression is equivalent to (x + 5)²?

Accepted Answer

x² + 10x + 25

Answer

(x + 5)² = x² + 2(5)x + 5² = x² + 10x + 25.

Question 3

A car travels at a constant speed of 60 mph. Which equation gives distance d after t hours?

Accepted Answer

d = 60t

Answer

Distance equals rate times time, so d = 60t.

Question 4

What are the x-intercepts of y = x² − x − 6?

Accepted Answer

x = 3 and x = −2

Answer

Factor as (x − 3)(x + 2) = 0, so x = 3 or x = −2.

Question 5

Simplify: (4x³ − 2x² + x) ÷ (2x)

Accepted Answer

2x² − x + 1/2

Answer

Divide each term by 2x: 4x³/2x = 2x², −2x²/2x = −x, x/2x = 1/2.

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