Solving Linear Systems of Equations

Front

What is a linear system of equations?

Back

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

Front

What does it mean to solve a system of equations?

Back

To solve a system of equations means to find the values of the variables that satisfy all equations in the system 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, where each point on the line represents a solution to the equation.

Front

What is the substitution method in solving linear systems?

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 systems?

Back

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

Front

What does it mean if a system of equations has no solution?

Back

A system of equations has no solution if the lines represented by the equations are parallel and never intersect.

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What does it mean if a system of equations has infinitely many solutions?

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

Front

Solve the system: x + 4y = -3 and x + 7y = -12.

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(9, -3)

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Solve the system: 3x + 2y = 16 and y = -7x + 19.

Back

(2, 5)

Front

Solve the system: x + 3y = 12 and y = \frac{2}{3}x + 1.

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(3, 3)