Solving Systems of Equations by Substitution

Front

What is a system of equations?

Back

A system of equations is a set of two or more 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, perform inverse operations to get the variable alone on one side of the equation.

Front

What is the first step in solving the system: y = 6x - 11 and -2x - 3y = -7?

Back

Substitute the expression for y from the first equation into the second equation.

Front

What is the solution to the system: y = 5x - 7 and -3x - 2y = -12?

Back

The solution is (2, 3).

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What does it mean if two lines are parallel in a system of equations?

Back

If two lines are parallel, they have no points of intersection, meaning there is no solution to the system.

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What does it mean if two lines intersect at one point in a system of equations?

Back

If two lines intersect at one point, the system has a unique solution, which is the coordinates of the intersection point.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of the lines of the equations plotted on a coordinate plane.

Front

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

Back

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

Front

What is the solution to the system: y = 2x + 1 and y = 4x - 1?

Back

The solution is (1, 3).