Algebra Flashcards

What is the y-intercept of the line y = 3x - 5?

Answer: -5

In slope-intercept form y = mx + b, the y-intercept is b = -5.

Solve the system: x + y = 10 and x - y = 4

Answer: x = 7, y = 3

Adding the two equations gives 2x = 14, so x = 7, then y = 10 - 7 = 3.

Simplify: (3x²y)(2xy³)

Answer: 6x³y⁴

Multiply coefficients (3 × 2 = 6) and add exponents for like bases: x²⁺¹ = x³ and y¹⁺³ = y⁴.

Which value of x satisfies the equation |2x - 4| = 6?

Answer: x = 5 or x = -1

Setting 2x - 4 = 6 gives x = 5; setting 2x - 4 = -6 gives x = -1.

What is the vertex of the parabola y = (x - 3)² + 2?

Answer: (3, 2)

In vertex form y = (x - h)² + k, the vertex is (h, k) = (3, 2).

If 2^x = 32, what is x?

Answer: 5

Since 32 = 2^5, x = 5.