Substitution

Front

What is substitution in solving systems of equations?

Back

Substitution is a method used to solve systems of equations by replacing one variable with an expression derived from another equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the first step in solving a 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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you substitute a variable in an equation?

Back

To substitute a variable, replace the variable in the equation with the expression that you found from another equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean to solve for y in terms of x?

Back

It means to express y as a function of x, typically in the form y = mx + b.

Tags

CCSS.6.EE.C.9

Front

What is the purpose of solving systems of equations?

Back

The purpose is to find the values of the variables that satisfy all equations in the system simultaneously.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is an example of a system of equations?

Back

y = 2x + 3 and y = -x + 1.

Tags

CCSS.8.EE.C.8B

Front

What is the solution to the system y = 2x + 3 and y = -x + 1?

Back

The solution is the point where the two lines intersect, which can be found by substituting one equation into the other.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the graphical interpretation of a system of equations?

Back

The graphical interpretation is that each equation represents a line, and the solution is the point(s) where the lines intersect.

Tags

CCSS.8.EE.C.8B

Front

What happens if the lines in a system of equations are parallel?

Back

If the lines are parallel, there is no solution because the lines never intersect.

Tags

CCSS.8.EE.C.8A

Front

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

Back

It means that the equations represent the same line, and every point on that line is a solution.

Tags

CCSS.8.EE.C.8A