Graphing Systems of Linear Equations

These flashcards cover key concepts related to graphing systems of linear equations, including solutions, interpretations of no solutions and infinite solutions, and properties like slope.

What is the solution for the equations 6x - 3y = -30 and 4x + 4y = 4?

(−3, 4)

What does it mean if a linear system has no solution?

The lines represented by the equations are parallel and do not intersect.

When does a system of linear equations have infinite solutions?

When the equations represent the same line in the graph.

For the equation y = −1/2 x + 4, what is the slope?

The slope is -1/2.

What can you conclude if the equations 12x - 4y = 0 and 2x + 2y = 8 have the same slope and y-intercept?

The system has infinite solutions.

What should you write if a solution exists for the equations 22 - y = -8 and 5x - 5y = -15?

An ordered pair (x, y) based on the intersection point.