Unit 4 Review - Systems of Equations

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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 point(s) where the equations intersect.

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How do you solve a system of equations graphically?

Back

To solve graphically, plot each equation on the same graph. The point(s) where the lines intersect represent the solution(s) to the system.

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

Back

It means the lines are parallel and will never intersect. This indicates that there is no set of values for the variables that satisfies all equations.

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

Back

It means the equations represent the same line, so every point on the line is a solution.

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What is the substitution method for solving systems of equations?

Back

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?

Back

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

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How can you determine if two equations represent the same line?

Back

If the equations can be transformed into each other by multiplying or dividing by a constant, they represent the same line.

Front

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

Back

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How do you find the y-intercept of a linear equation?

Back

Front

What is the significance of the coefficients in a linear equation?

Back

The coefficients represent the rate of change (slope) and the constant term represents the y-intercept of the line.