System of Linear Equations in Two Variables

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What is a system of linear equations in two variables?

Back

A system of linear equations in two variables consists of two or more linear equations that share the same variables, typically represented as x and y.

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What does it mean if the graph of a system of equations shows parallel lines?

Back

If the graph shows parallel lines, it means that the system has no solution because the lines never intersect.

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What indicates that a system of linear equations has exactly one solution?

Back

A system has exactly one solution if the graph of the equations shows intersecting lines.

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What is the significance of the slope in a system of linear equations?

Back

The slope indicates the steepness of the line; if two lines have the same slope but different y-intercepts, they are parallel and do not intersect.

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How can you determine if a system of equations is consistent or inconsistent?

Back

A system is consistent if it has at least one solution (intersecting lines) and inconsistent if it has no solutions (parallel lines).

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What is the graphical representation of the equations x - y = 1 and 2x - y = 1?

Back

The graphical representation shows two intersecting lines, indicating that the system has one unique solution.

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What does the ordered pair (15, 7) represent in the context of a word problem involving costs?

Back

The ordered pair (15, 7) represents the quantities of two items (e.g., illustration boards and markers) that satisfy the equations derived from the problem.

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What is the y-intercept in a linear equation?

Back

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

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How do you solve a system of linear equations using substitution?

Back

To solve by substitution, solve one equation for one variable and substitute that expression into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.