Flashcard Solving Systems of Equations

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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 set of values that satisfy all equations simultaneously.

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

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Solving by substitution involves solving one equation for one variable and then substituting that expression into the other equation.

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The solution is (4, 6). Substitute y = 6 into the second equation to find x.

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

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It means that the lines represented by the equations are parallel and do not intersect.

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The solution is (-5, -7). Use substitution to find the values of x and y.

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What is the significance of the number of solutions in a system of equations?

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The number of solutions indicates the relationship between the equations: one solution (intersecting lines), no solution (parallel lines), or infinitely many solutions (same line).

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

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If the equations are equivalent (one can be derived from the other), they represent the same line, resulting in infinitely many solutions.

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The solution is (-3, -3). Use substitution or elimination to solve.

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What is the graphical representation of a system of equations?

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The graphical representation consists of lines on a coordinate plane, where the intersection point(s) represent the solution(s) of the system.