Solving Systems of Equations

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What is a system of equations?

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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 to solve a system of equations?

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To solve a system of equations means to find the values of the variables that satisfy all equations in the system simultaneously.

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What is the substitution method in 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 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 variable.

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How do you represent a linear equation in slope-intercept form?

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A linear equation in slope-intercept form is represented as y = mx + b, where m is the slope and b is the y-intercept.

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What is the slope of a line?

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The slope of a line is a measure of its steepness, calculated as the rise over run (change in y over change in x).

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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 lines represented by the equations are parallel and never intersect.

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

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A system of equations has infinitely many solutions when the equations represent the same line, meaning they intersect at every point on that line.

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How can you check if your solution to a system of equations is correct?

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You can check your solution by substituting the values back into the original equations to see if they hold true.

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What is a consistent system of equations?

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A consistent system of equations is one that has at least one solution, meaning the lines intersect at one or more points.