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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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.

Tags

CCSS.8.EE.C.8B

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.

Tags

CCSS.8.EE.C.8A

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.

Tags

CCSS.8.EE.C.8A

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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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.

Tags

CCSS.8.EE.B.5

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.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

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.