4-4 Advanced Practice

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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 to the system is the set of values that satisfy all equations simultaneously.

Front

What does it mean for a system of equations to be in standard form?

Back

Front

How do you convert an equation to standard form?

Back

To convert an equation to standard form, rearrange the equation to isolate the variables on one side and the constant on the other, ensuring that the coefficients are integers.

Front

What is the graphical representation of a system of equations?

Back

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 does it mean if two lines intersect at one point?

Back

If two lines intersect at one point, it means the system of equations has a unique solution, which is the coordinates of the intersection point.

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What does it mean if two lines are parallel?

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If two lines are parallel, it means the system of equations has no solution, as the lines never intersect.

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What does it mean if two lines coincide?

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If two lines coincide, it means the system of equations has infinitely many solutions, as every point on the line is a solution.

Front

How do you find the solution to a system of equations graphically?

Back

To find the solution graphically, plot both equations on the same coordinate plane and identify the point(s) where the lines intersect.

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What is the substitution method for solving systems of equations?

Back

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

Front

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 remaining variable.