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 remaining variable.

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What is point-slope form of a linear equation?

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Point-slope form is an equation of a line written as y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

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How do you convert from standard form to slope-intercept form?

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To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y in terms of x.

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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 two lines to be parallel?

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Two lines are parallel if they have the same slope and will never intersect.

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What does it mean for two lines to be perpendicular?

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Two lines are perpendicular if the product of their slopes is -1, meaning they intersect at a right angle.

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

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To check if a solution is correct, substitute the values of the variables back into the original equations to see if they hold true.