Systems of Equations

Front

What is a system of equations?

Back

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean if a system of equations has one solution?

Back

The graphs of the equations intersect at exactly one point.

Tags

CCSS.8.EE.C.8A

Front

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

Back

The graphs of the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if a system of equations has infinitely many solutions?

Back

The equations represent the same line, so they intersect at every point on that line.

Tags

CCSS.8.EE.C.8A

Front

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

Back

By analyzing the slopes and y-intercepts of the lines represented by the equations.

Tags

CCSS.8.EE.C.8B

Front

What is the slope of the line represented by the equation y = mx + b?

Back

The slope is 'm', which indicates the steepness and direction of the line.

Tags

CCSS.8.EE.B.5

Front

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

Back

The y-intercept is 'b', the point where the line crosses the y-axis.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

How do you solve a system of equations using substitution?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you solve a system of equations using elimination?

Back

Add or subtract the equations to eliminate one variable, then solve for the remaining variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the graphical representation of the equation y = 2x + 1?

Back

A straight line with a slope of 2 and a y-intercept of 1.