Understanding Simultaneous Equations

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What are simultaneous equations?
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Simultaneous equations are a set of equations with multiple variables that are solved together.
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What is the substitution method for solving simultaneous equations?
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The substitution method involves solving one equation for one variable, then substituting that expression into the other equation.
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How does the elimination method work?
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The elimination method involves adding or subtracting equations to eliminate one of the variables.
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What is the graphical method of solving simultaneous equations?
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The graphical method involves plotting each equation on a graph and identifying the intersection point.
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What does it mean if two lines on a graph are parallel when solving simultaneous equations?
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If two lines are parallel, it means the equations have no solution because they never intersect.
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What does it mean if two lines coincide on a graph?
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If two lines coincide, it means the equations are dependent and have infinitely many solutions.
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How do you recognize a consistent system of equations?
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A consistent system has at least one solution where the lines intersect at a point or coincide.
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How do you recognize an inconsistent system of equations?
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An inconsistent system has no solution, typically represented by parallel lines that never intersect.
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What are linear simultaneous equations?
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Linear simultaneous equations are equations of the first degree involving two or more variables solved together.
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How can simultaneous equations be used in real-life scenarios?
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Simultaneous equations can model real-life problems such as budgeting, mixture problems, and comparing rates.
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What is the coefficient in a linear equation?
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The coefficient is the numerical factor multiplied by a variable in an equation.
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What do you do if one equation is already solved for a variable in the substitution method?
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If one equation is solved for a variable, you can directly substitute that expression in the other equation.
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How do you use addition in the elimination method?
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To use addition in elimination, you add two equations to cancel out one variable after aligning their coefficients.
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How can you check the solution of simultaneous equations?
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Substitute the solution back into the original equations to verify each equation holds true.
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What role does normalization play in the substitution method?
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Normalization may involve manipulating one equation to simplify a variable, making substitution easier.
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