CA1 Solving Linear Systems Review

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What is a linear system of equations?

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A linear system of equations is a collection of two or more linear equations involving the same variables. The solution is the set of values that satisfy all equations simultaneously.

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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 make all equations in the system true at the same time.

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What is the graphical representation of a linear equation?

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The graphical representation of a linear equation is a straight line on a coordinate plane, where each point on the line represents a solution to the equation.

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What is the substitution method in solving linear systems?

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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 linear systems?

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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 does it mean if a system of equations has no solution?

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A system of equations has no solution if the equations represent parallel lines that never intersect.

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

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A system of equations has infinitely many solutions if the equations represent the same line, meaning every point on the line is a solution.

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How do you determine the solution of a system of equations graphically?

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The solution of a system of equations can be determined graphically by finding the point(s) where the lines representing the equations intersect.

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What is the point of intersection in a system of equations?

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The point of intersection is the point where the graphs of the equations meet, representing the solution to the system.

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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.