Solving pairs of linear equations in two variables

Front

What is a linear equation in two variables?

Back

A linear equation in two variables is an equation that can be written in the form ax + by = c, where a, b, and c are constants, and x and y are variables.

Front

What does it mean to solve a pair of linear equations?

Back

To solve a pair of linear equations means to find the values of the variables that satisfy both equations simultaneously.

Front

What is the graphical representation of a linear equation?

Back

The graphical representation of a linear equation is a straight line on a coordinate plane.

Front

What is the substitution method in solving linear 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 in solving linear equations?

Back

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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How can you check if your solution to a pair of linear equations is correct?

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You can check your solution by substituting the values of the variables back into both original equations to see if they hold true.

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What is the meaning of 'consistent' and 'inconsistent' systems of equations?

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A consistent system has at least one solution, while an inconsistent system has no solutions.

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What is the meaning of 'dependent' and 'independent' systems of equations?

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Dependent systems have infinitely many solutions (the equations represent the same line), while independent systems have exactly one solution (the lines intersect at one point).

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

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the x-intercept of a linear equation?

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To find the x-intercept, set y = 0 in the equation and solve for x.