Solutions to linear system from graphs

Front

What is a linear system of equations?

Back

A set of two or more linear equations with the same variables.

Front

What does it mean for a linear system to have a solution?

Back

A solution is a set of values for the variables that makes all equations in the system true.

Front

What is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane.

Front

How can you find the solution to a system of equations graphically?

Back

By identifying the point where the lines intersect on the graph.

Front

What does it mean if two lines are parallel in a linear system?

Back

The system has no solution because the lines never intersect.

Front

What does it mean if two lines coincide in a linear system?

Back

The system has infinitely many solutions because the lines are the same.

Front

What is the solution to the system of equations represented by the lines y = 2x + 1 and y = -x + 4?

Back

(1, 3) - The point where the two lines intersect.

Front

What is the slope of a line in the equation y = mx + b?

Back

The slope (m) represents the rate of change of y with respect to x.

Front

What is the y-intercept in the equation y = mx + b?

Back

The y-intercept (b) is the point where the line crosses the y-axis.

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.