System 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?

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To solve a system of equations means to find the values of the variables that satisfy all equations in the system 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 remaining variable.

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How do you determine if a system of equations has no solution?

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A system has no solution if the equations represent parallel lines, which means they never intersect.

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How do you determine if a system of equations has infinitely many solutions?

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A system has infinitely many solutions if the equations represent the same line, meaning they overlap completely.

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What is the graphical representation of a system of equations?

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The graphical representation is the intersection point(s) of the lines represented by the equations on a coordinate plane.

Front

Solve the system of equations: -4x - 3y = 19 and 2x - 6y = -14.

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(-4,-1)

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Solve the system of equations: x + 5y = -18 and 2x + 2y = -4.

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(2,4)

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Solve the system of equations: x + 4y = -3 and x + 7y = -12.

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(9,-3)