Math 1 Benchmark 2 Review Part 2

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What is a system of equations?

Back

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

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

Back

It means that the equations represent parallel lines that never intersect, indicating that there are no common solutions.

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How do you represent a word problem as a system of equations?

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Identify the variables, translate the relationships and conditions into equations, and ensure the equations reflect the problem's constraints.

Front

What is the slope-intercept form of a linear equation?

Back

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How do you solve a system of equations by graphing?

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Graph each equation on the same coordinate plane and identify the point(s) where the lines intersect. This point(s) is the solution.

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What is the significance of the y-intercept in a linear equation?

Back

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What does it mean for a point to be a solution to a system of equations?

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A point is a solution if it satisfies all equations in the system, meaning it makes all equations true when substituted.

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How can you determine if a point is a solution to a linear equation?

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Substitute the x and y values of the point into the equation. If both sides of the equation are equal, the point is a solution.

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What is the method of substitution in solving systems of equations?

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The method of substitution involves solving one equation for one variable and then substituting that expression into the other equation.

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What is the method of elimination in solving systems of equations?

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The method of elimination involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.