Systems of Equations - Review

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

Tags

CCSS.8.EE.C.8B

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What does it mean for a system of equations to have no solution?

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A system of equations has no solution when the graphs of the equations are parallel lines, meaning they never intersect.

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CCSS.8.EE.C.8A

Front

What is the graphical representation of intersecting lines in a system of equations?

Back

Intersecting lines represent a system of equations that has exactly one solution, which is the point of intersection.

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CCSS.8.EE.C.8A

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How do you solve a system of equations using substitution?

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To solve by substitution, solve one equation for one variable, then substitute that expression into the other equation.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What is the elimination method in solving systems of equations?

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What does it mean for a system of equations to be consistent?

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A consistent system has at least one solution, which can be either one solution (intersecting lines) or infinitely many solutions (coincident lines).

Tags

CCSS.8.EE.C.8B

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What is the solution to the system of equations 2x + 3y = 6 and x - y = 1?

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The solution is (3, 0).

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

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CCSS.8.EE.B.6

CCSS.8.F.A.3

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

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If the slopes are equal and the y-intercepts are different, there are no solutions. If the slopes are different, there is one solution. If the slopes and y-intercepts are equal, there are infinitely many solutions.

Tags

CCSS.8.EE.C.8B

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What is the y-intercept of the equation y = 2x + 3?

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The y-intercept is 3, which is the point where the line crosses the y-axis.

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CCSS.8.EE.B.6

CCSS.8.F.A.3