Systems of equations

Front

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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What does it mean to solve a system of equations graphically?

Back

To solve a system of equations graphically means to plot the equations on a graph and find the point(s) where they intersect, which represents the solution.

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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.

Front

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.

Front

How do you find the perimeter of a rectangle?

Back

The perimeter of a rectangle is found using the formula P = 2(length + width).

Front

If the length of a rectangle is 4 more than its width, how can you express this relationship mathematically?

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If width = w, then length = w + 4.

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What is the solution to the system of equations 7x + 4y = 12 and x + 2y = -4?

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The solution is (4, -4).

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How do you check if a solution is correct for a system of equations?

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Substitute the solution values into both equations. If both equations are true, the solution is correct.

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What does it mean for two equations to be independent?

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Two equations are independent if they have exactly one solution, meaning their graphs intersect at one point.

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What does it mean for two equations to be dependent?

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Two equations are dependent if they represent the same line, meaning they have infinitely many solutions.