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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 is the point(s) where the equations intersect on a graph.

Tags

CCSS.8.EE.C.8B

Front

How do you solve a system of linear equations using substitution?

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To solve using substitution, solve one equation for one variable, then substitute that expression into the other equation to find the value of the second variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the graphical representation of a system of linear equations?

Back

The graphical representation is the intersection point(s) of the lines representing each equation. If they intersect at one point, there is one solution; if they are parallel, there are no solutions; if they are the same line, there are infinitely many solutions.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if two lines are parallel in a system of equations?

Back

If two lines are parallel, it means that the system of equations has no solution, as the lines never intersect.

Tags

CCSS.8.EE.C.8A

Front

What is the elimination method for solving systems of 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 solution to the system of equations 2x + y = 40 and x - 2y = -20?

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The solution is x = 12, y = 16.

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CCSS.HSA.REI.C.9

Front

How can you determine if a point is a solution to a system of equations?

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To determine if a point is a solution, substitute the x and y values of the point into each equation. If both equations are satisfied, the point is a solution.

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

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The coefficients represent the rate of change of the dependent variable with respect to the independent variable. They determine the slope of the line when graphed.

Tags

CCSS.8.EE.B.5

Front

How do you interpret the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x = 0. It represents the point where the line crosses the y-axis.

Tags

CCSS.HSF.LE.B.5

Front

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

Back

The slope indicates the steepness of the line and the direction of the relationship between the variables. A positive slope means the line rises, while a negative slope means it falls.

Tags

CCSS.8.EE.B.5