Solve Systems of Linear Equations

Front

What is a system of linear equations?

Back

A system of linear equations is a set of two or more linear equations with the same variables. The solution is the point(s) where the equations intersect.

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What does it mean for a system of equations to be consistent?

Back

A consistent system of equations has at least one solution, meaning the lines represented by the equations intersect at one or more points.

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What does it mean for a system of equations to be inconsistent?

Back

An inconsistent system of equations has no solutions, meaning the lines represented by the equations are parallel and never intersect.

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, where the x and y coordinates satisfy the equation.

Front

How can you determine the solution to a system of equations graphically?

Back

The solution to a system of equations can be determined graphically by finding the point(s) where the lines intersect.

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What is substitution method in solving systems of equations?

Back

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 elimination method in 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.

Front

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

Back

The slope-intercept form of a linear equation is given by 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?

Back

The slope (m) of a line given two points (x1, y1) and (x2, y2) is calculated as m = (y2 - y1) / (x2 - x1).

Front

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.