Pathways Ch. 3C (Systems)

Front

What is a system of equations?

Back

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

Front

What does it mean to find the solution to a system of equations?

Back

It means to find the values of the variables that satisfy all equations in the system simultaneously.

Front

What is the y-intercept of a linear equation?

Back

The y-coordinate of the point where the line crosses the y-axis, found by setting x=0 in the equation.

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 is the slope of a line?

Back

The rate at which y changes for a unit change in x, often represented as 'm' in the equation y = mx + b.

Front

What is the standard form of a linear equation?

Back

Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

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

Back

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

Front

What is the graphical representation of a system of equations?

Back

It is the intersection point(s) of the lines represented by the equations on a coordinate plane.

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into each equation; if all equations are satisfied, it is a solution.

Front

What is the combined equation of the system: 5x - 4y = 11 and 5x + 4y = -14?

Back

10x = -3.