Solve systems of equations by graphing or substitution

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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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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

Back

A point is a solution to a system of equations if it satisfies all equations in the system when substituted into them.

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

Back

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

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What is the graphical representation of a system of equations?

Back

The graphical representation of a system of equations consists of the graphs of the equations plotted on the same coordinate plane.

Tags

CCSS.8.EE.C.8B

Front

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

Back

If two lines are parallel, they have no points of intersection, meaning there is no solution to the system of equations.

Tags

CCSS.8.EE.C.8B

Front

What does it mean if two lines in a system of equations are the same line?

Back

If two lines are the same, they overlap completely, resulting in infinite solutions to the system of equations.

Tags

CCSS.8.EE.C.8A

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What is the substitution method for solving systems of 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 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 other variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the solution to the system of equations y = 4x + 5 and y = x - 4?

Back

The solution is the point where the two lines intersect, which can be found by setting the equations equal to each other.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you graph a linear equation?

Back

To graph a linear equation, find two or more points that satisfy the equation and plot them on a coordinate plane, then draw a line through the points.