PRACTICE FLASHCARD for Flashcard #5 - 2nd Qtr - ALG

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that can be solved together.

Front

How do you solve a system of equations using substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

Front

What does an ordered pair represent in a coordinate system?

Back

An ordered pair (x, y) represents a point on the Cartesian plane, where 'x' is the horizontal position and 'y' is the vertical position.

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.

Front

How do you find the slope of a line given two points?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the meaning of 'y-intercept' in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of 'b' in the slope-intercept form.

Front

What is the process of elimination in solving systems of equations?

Back

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

Front

What does it mean for a system of equations to be consistent?

Back

A consistent system has at least one solution, meaning the equations intersect at one or more points.

Front

What is an inconsistent system of equations?

Back

An inconsistent system has no solutions, meaning the equations represent parallel lines that never intersect.

Front

How do you graph a linear equation?

Back

1. Identify the slope and y-intercept. 2. Plot the y-intercept on the graph. 3. Use the slope to find another point. 4. Draw a line through the points.