[3] U5D8 Review Mix

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What is a system of equations?

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A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect on a graph.

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What does it mean for a system of equations to have no solution?

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A system of equations has no solution when the graphs of the equations are parallel, meaning they never intersect.

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How do you find the value of x in a system of equations?

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To find the value of x, you can use substitution or elimination methods to solve the equations simultaneously.

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What is the substitution method in 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 in 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 other variable.

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

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A consistent system of equations has at least one solution, meaning the graphs of the equations intersect at one or more points.

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

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An inconsistent system of equations has no solutions, meaning the equations represent parallel lines that never intersect.

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How can you determine the number of solutions in a system of equations graphically?

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Graph the equations; if they intersect at one point, there is one solution; if they are parallel, there are no solutions; if they are the same line, there are infinitely many solutions.

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What is the graphical representation of a linear equation?

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A linear equation is represented graphically as a straight line on a coordinate plane.

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

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