Solving Systems Using Graphing and 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, you perform inverse operations to get the variable on one side of the equation by itself.

Front

What is the substitution method?

Back

The substitution method is a technique for solving systems of equations where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

Solve the system: y = 2x + 3 and y = 5x.

Back

(1, 5)

Front

Solve the system: 5x - 3y = -2 and y = 4.

Back

(2, 4)

Front

What is the graphical representation of a system of equations?

Back

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

Front

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

Back

If two lines are parallel, it means there is no solution to the system, as the lines never intersect.

Front

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

Back

If two lines coincide, it means there are infinitely many solutions, as they are the same line.

Front

Solve the system: -5x - 4y = -9 and y = 6.

Back

(-3, 6)