Solving Systems of Equations

Front

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.

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What does it mean for a system of equations to have a unique solution?

Back

A unique solution occurs when the graphs of the equations intersect at exactly one point.

Front

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

Back

No solution occurs when the graphs of the equations are parallel and never intersect.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

Infinitely many solutions occur when the equations represent the same line, meaning they coincide.

Front

How do you graph a linear equation?

Back

To graph a linear equation, find two or more points that satisfy the equation and connect them with a straight line.

Front

What is the substitution method for solving systems of equations?

Back

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

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What is the elimination method for 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.

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

Back

Substitute the point's coordinates into both equations. If both equations are true, the point is a solution.

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

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The slope represents the rate of change of y with respect to x; it indicates how steep the line is.