Solve Systems by Substitution

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 to solve a system of equations by substitution?

Back

It involves solving one equation for one variable and substituting that expression into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the first step in solving a system of equations by substitution?

Back

Isolate one variable in one of the equations.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

The lines represented by 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, meaning every point on the line is a solution.

Tags

CCSS.8.EE.C.8A

Front

How do you check if your solution to a system of equations is correct?

Back

Substitute the solution back into both original equations to see if they hold true.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the solution to the system: y = 2x + 3 and y = -x + 1?

Back

(2, 7) - found by substituting x=2 into either equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the graphical representation of a system of equations?

Back

The intersection point(s) of the lines representing the equations.

Tags

CCSS.8.EE.C.8A

Front

What is the significance of the slope in a linear equation?

Back

It indicates the steepness and direction of the line; positive slope means the line rises, negative means it falls.

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept in a linear equation?

Back

The point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.