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What is a system of linear equations?

Back

A system of linear equations is a set of two or more linear equations with the same variables. The solution to the system is the point(s) where the equations intersect.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean to solve a system of linear equations graphically?

Back

Solving a system of linear equations graphically involves plotting the equations on a coordinate plane and identifying the point(s) where the lines intersect, which represents the solution.

Tags

CCSS.8.EE.C.8B

Front

What is the elimination method for solving systems of linear equations?

Back

The elimination method involves adding or subtracting 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

What is the substitution method for solving systems of linear equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the significance of the solution (0, 5) in the context of a system of equations?

Back

The solution (0, 5) indicates that when x = 0, y = 5 satisfies both equations in the system.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you determine 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, meaning they never intersect.

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.

Tags

CCSS.8.EE.C.8A

Front

What is the role of coefficients in a linear equation?

Back

Coefficients are the numerical factors that multiply the variables in a linear equation, determining the slope and position of the line.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

How can you use multiplication to solve a system of equations?

Back

You can multiply one or both equations by a number to create equivalent equations that can be solved more easily, often used in the elimination method.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the graphical representation of the equation y = 4x + 1?

Back

The equation y = 4x + 1 represents a straight line with a slope of 4 and a y-intercept of 1.