Solving Systems of Linear Equations

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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 three possible outcomes when solving a system of linear equations?

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1. One solution (the lines intersect at one point). 2. No solution (the lines are parallel). 3. Infinitely many solutions (the lines coincide).

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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 do 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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How do you determine if a system of equations has infinitely many solutions?

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A system has infinitely many solutions if the equations represent the same line, meaning they have the same slope and y-intercept.

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What is the graphical representation of a system of linear equations?

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The graphical representation is the intersection of the lines corresponding to the equations. The intersection point(s) represent the solution(s).

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What is the first step in solving the system of equations 3x + 2y = 16 and 7x + y = 19?

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You can use either substitution or elimination. For substitution, solve one equation for y and substitute into the other.

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Solve the system of equations: 4x - 3y = 5 and y = 2x - 3.

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(2, 1) is the solution.