Topic 4 Study Guide 24-25

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

Front

Solve the system of equations using elimination: 5x + 4y = 38 and 6x + 3y = 42.

Back

(6, 2)

Front

What does it mean if a system of equations has no solution?

Back

It means that the lines represented by the equations are parallel and never intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

It means that the equations represent the same line, and every point on that line is a solution.

Front

Solve by graphing: y = -2x + 3 and 4x + 2y = -8. What is the solution?

Back

No solution.

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables.

Front

How do you graph a linear inequality?

Back

Graph the corresponding linear equation as a dashed or solid line, then shade the appropriate region based on the inequality.

Front

What is the difference between a solid line and a dashed line when graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution (≥ or ≤), while a dashed line indicates they are not (> or <).

Front

Solve by graphing: y = -2x + 3 and 2x + y = 3. What is the solution?

Back

Infinitely many solutions.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.