Solving System of Equations by graphing

Front

What is a system of equations?

Back

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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How can you solve a system of equations graphically?

Back

To solve a system of equations graphically, you graph each equation on the same coordinate plane and identify the point(s) where the lines intersect.

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What does it mean if two lines intersect at a single point?

Back

If two lines intersect at a single point, it means there is a unique solution to the system of equations represented by those lines.

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What does it mean if two lines are parallel?

Back

If two lines are parallel, it means they have no points of intersection and therefore the system of equations has no solution.

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What does it mean if two lines coincide?

Back

If two lines coincide, it means they lie on top of each other, resulting in infinitely many solutions to the system of equations.

Front

What is the graphical representation of the solution (1, 3)?

Back

The point (1, 3) is the intersection point of the two lines representing the equations in the system.

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How do you determine the solution from a graph?

Back

To determine the solution from a graph, locate the point where the lines intersect; this point's coordinates are the solution to the system.

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

Back

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

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What is the slope of a line, and how does it affect the graph?

Back

The slope of a line indicates its steepness and direction. A positive slope rises from left to right, while a negative slope falls.

Front

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

Back

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