Solving Linear and Quadratic Systems

Front

What method is commonly used when solving linear-quadratic systems algebraically?

Back

Substitution

Front

Given the system of equations: y = x² + 3x - 5 and y = x + 3, what is the value of y when x = 2?

Back

5

Front

What are the solutions to the equation x² + 2x - 8 = 0?

Back

x = -4 and x = 2

Front

Which equation can be used to solve the system: y = x² + 3x - 5 and y = x + 3?

Back

x² + 3x - 5 = x + 3

Front

Find the solutions for the system: y = x² - 4x + 6 and y = x + 2.

Back

(1, 3) and (4, 6)

Front

What is a linear equation?

Back

An equation that makes a straight line when graphed, typically in the form y = mx + b.

Front

What is a quadratic equation?

Back

An equation that can be expressed in the form ax² + bx + c = 0, where a ≠ 0.

Front

What does the term 'substitution' mean in solving equations?

Back

Replacing one variable with an expression involving another variable.

Front

What is the purpose of the elimination method in solving systems of equations?

Back

To eliminate one variable by adding or subtracting equations.

Front

How do you find the vertex of a quadratic function?

Back

Use the formula x = -b/(2a) to find the x-coordinate, then substitute back to find the y-coordinate.