Solve Systems of Linear Equations by Substitution

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.

Front

What does it mean to solve a system of equations by substitution?

Back

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

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform inverse operations to get the variable on one side of the equation by itself.

Front

What is the first step in solving the system of equations by substitution?

Back

The first step is to solve one of the equations for one variable in terms of the other variable.

Front

If you have the equations y = 2x + 3 and 4x + y = 11, how do you solve them by substitution?

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Substitute y from the first equation into the second: 4x + (2x + 3) = 11, then solve for x.

Front

What is the solution to the system of equations y = 2x + 3 and 4x + y = 11?

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The solution is (2, 7).

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

Back

A system 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 has infinitely many solutions if the equations represent the same line, meaning they intersect at every point on that line.

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

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You can check by substituting the solution back into the original equations to see if both equations are satisfied.

Front

What is the graphical representation of a system of linear equations?

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The graphical representation is the intersection point(s) of the lines on a coordinate plane.