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.

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How do you solve a system of equations graphically?

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To solve a system of equations graphically, plot each equation on the same graph and identify the point(s) where the lines intersect. This point(s) represents the solution.

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

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If two lines are parallel, they have the same slope and will never intersect, meaning there is no solution to the system.

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

Back

The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept.

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How can you determine if a system of equations has one solution, no solution, or infinitely many solutions?

Back

A system has one solution if the lines intersect at one point, no solution if the lines are parallel, and infinitely many solutions if the lines are the same (coincident).

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What is the substitution method for solving systems of equations?

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The substitution method involves solving one equation for one variable and then 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 variable.

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What does the point (x, y) represent in the context of a system of equations?

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The point (x, y) represents the solution to the system of equations, indicating the values of the variables that satisfy all equations in the system.

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How do you find the x-intercept of a linear equation?

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To find the x-intercept, set y = 0 in the equation and solve for x.

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How do you find the y-intercept of a linear equation?

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To find the y-intercept, set x = 0 in the equation and solve for y.