Solving Systems by Graphing, Substitution & Elimination

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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.

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What does it mean to solve a system of equations by graphing?

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Solving by graphing involves plotting each equation on the same coordinate plane and identifying the point(s) where they intersect.

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

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A system has no solution if the lines represented by the equations are parallel, meaning 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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Multiply the first equation by 3 and the second equation by 4 to align the coefficients of x.

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Multiply the equation by -4.

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The solution is (-4, -2).

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The solution is (-6, 7).