Solving Systems of Equations by Graphing (PA)

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect on a graph.

Front

What does it mean to solve a system of equations by graphing?

Back

Solving a system of equations by graphing involves plotting each equation on the same set of axes and identifying the point(s) where the graphs intersect.

Front

What is the solution to the system of equations: y = x + 1 and y = -3x + 9?

Back

(2, 3)

Front

What is the solution to the system of equations: y = x - 2 and y = -2x + 1?

Back

(1, -1)

Front

How can you determine the number of solutions in a system of equations?

Back

The number of solutions can be determined by the intersection of the graphs: one solution (intersecting), no solution (parallel lines), or infinitely many solutions (same line).

Front

What is the solution to the system of equations: y = \frac{1}{3}x + 2 and y = -x + 10?

Back

(6, 4)

Front

Is (1, 4) a solution for the system: y = 2x + 2 and y = x + 5?

Back

No, (1, 4) does not satisfy both equations.

Front

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

Back

If two lines are parallel, it means they have the same slope and will never intersect, resulting in no solution for the system.

Front

What does it mean if two lines are the same in a system of equations?

Back

If two lines are the same, they have infinitely many solutions because every point on the line is a solution to the system.

Front

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

Back

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