Solve systems of equations by graphing or substitution

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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 for a point to be a solution to a system of equations?

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A point is a solution to a system of equations if it satisfies all equations in the system when substituted into them.

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How can you determine if a point is a solution to a system of equations?

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To determine if a point is a solution, substitute the x and y values of the point into each equation. If both equations are true, the point is a solution.

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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 consists of the graphs of the equations plotted on the same coordinate plane.

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

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If two lines are parallel, they have no points of intersection, meaning there is no solution to the system of equations.

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What does it mean if two lines in a system of equations are the same line?

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If two lines are the same, they overlap completely, resulting in infinite solutions to the system of equations.

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What is the substitution method for 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 for 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 solution to the system of equations y = 4x + 5 and y = x - 4?

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The solution is the point where the two lines intersect, which can be found by setting the equations equal to each other.

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How do you graph a linear equation?

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To graph a linear equation, find two or more points that satisfy the equation and plot them on a coordinate plane, then draw a line through the points.