Solving Systems of Equations

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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 to the system is the set of values that satisfy all equations simultaneously.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you solve a system of equations graphically?

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To solve a system of equations graphically, you plot each equation on the same coordinate plane and identify the point(s) where the lines intersect. This point(s) represents the solution(s) to the system.

Tags

CCSS.8.EE.C.8B

Front

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

Back

A system of equations has no solution if the lines represented by the equations are parallel and never intersect. This indicates that there are no values that satisfy both equations.

Tags

CCSS.8.EE.C.8A

Front

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

Back

A system of equations has infinitely many solutions if the equations represent the same line, meaning every point on the line is a solution to the system.

Tags

CCSS.8.EE.C.8B

Front

What is the substitution method for solving systems of equations?

Back

The substitution method involves solving one of the equations for one variable and then substituting that expression into the other equation to find the values of both variables.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the elimination method for solving systems of equations?

Back

The elimination method involves adding or subtracting the equations to eliminate one variable, making it easier to solve for the remaining variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you write a system of equations from a word problem?

Back

To write a system of equations from a word problem, identify the variables, translate the relationships and conditions described in the problem into equations, and ensure they represent the same situation.

Front

What is the significance of the point of intersection in a system of equations?

Back

The point of intersection represents the solution to the system of equations, indicating the values of the variables that satisfy all equations in the system.

Tags

CCSS.8.EE.C.8B

Front

How can you determine if two lines are parallel from their equations?

Back

Two lines are parallel if they have the same slope but different y-intercepts. In slope-intercept form (y = mx + b), if the values of m are equal and b is different, the lines are parallel.

Tags

CCSS.8.EE.B.5

Front

What is slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is given by the formula y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3