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 to the system is the point(s) where the equations intersect.

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What does it mean for a system of equations to have no solution?

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A system of equations has no solution when the graphs of the equations are parallel lines, meaning they never intersect.

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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 the point satisfies all equations, it is a solution.

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What is the graphical representation of a system of equations with one solution?

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The graphical representation of a system with one solution consists of two lines that intersect at a single point.

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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 does it mean for a system of equations to have infinitely many solutions?

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A system has infinitely many solutions when the equations represent the same line, meaning every point on the line is a solution.

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What is the slope-intercept form of a linear equation?

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The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

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How do you find the slope of a line given two points?

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The slope (m) can be found using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

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What is the significance of the y-intercept in a linear equation?

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The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is zero.