CP #4 Review | Systems of Linear Equations in Two Variables

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What is a system of linear equations?

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A system of linear equations is a set of two or more linear 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 are the possible types of solutions for a system of linear equations?

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1. One Solution: The lines intersect at a single point. 2. No Solution: The lines are parallel and never intersect. 3. Infinitely Many Solutions: The lines coincide.

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How do you represent a system of equations graphically?

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A system of equations can be represented graphically by plotting each equation on the same coordinate plane. The intersection points represent the solutions.

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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 remaining variable.

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How can you determine if a system of equations has no solution?

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A system has no solution if the equations represent parallel lines, which means they have the same slope but different y-intercepts.

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What does it mean if a system of equations has infinitely many solutions?

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If a system has infinitely many solutions, it means the equations represent the same line, and every point on that line is a solution.

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What is the standard form of a linear equation?

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

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