PreAlgebra - Module 4 - Target 25 - 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 point where the equations intersect on a graph.

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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 graphical representation of a system of equations?

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

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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 other variable.

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What does it mean if two lines are parallel in a system of equations?

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If two lines are parallel, it means they have no points of intersection, indicating that the system has no solution.

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What does it mean if two lines coincide in a system of equations?

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If two lines coincide, they lie on top of each other, indicating that there are infinitely many solutions to the system.

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What is the solution to the system of equations x - 4y = 16 and 5x + 4y = 8?

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The solution is (4, -3).

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What is the solution to the system of equations 5x - 4y = -16 and x + 2y = -6?

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The solution is (-4, -1).

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What is the solution to the system of equations x + y = 3 and 3x - y = 1?

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The solution is (1, 2).