Writing 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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How do you solve a system of equations using substitution?

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1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

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What is the graphical representation of a system of equations?

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The graphical representation is the intersection point(s) of the lines representing each equation on a coordinate plane.

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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, it means there is no solution to the system, as the lines never intersect.

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

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If two lines coincide, it means there are infinitely many solutions, as every point on the line is a solution.

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How can you determine the number of solutions in a system of equations?

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By analyzing the slopes and y-intercepts of the lines: 1. Different slopes = one solution. 2. Same slope, different intercepts = no solution. 3. Same slope, same intercept = infinitely many solutions.

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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 is the standard form of a linear equation?

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The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

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How do you convert a linear equation 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 change in y divided by the change in x (rise/run).