Solve 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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, perform inverse operations to get the variable on one side of the equation and all other terms on the opposite side.

Tags

CCSS.7.EE.B.4A

Front

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

Back

Substitute x = 6 into the second equation: y = 2(6) - 3.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

The solution is (1, 3).

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

It means the lines represented by the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

Front

What is the graphical representation of a system of equations?

Back

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

Tags

CCSS.8.EE.C.8B

Front

What does it indicate if two equations represent the same line?

Back

It indicates that the system has infinitely many solutions, as every point on the line is a solution.

Tags

CCSS.8.EE.C.8B

Front

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

Back

Substitute the solution back into the original equations to see if both equations are satisfied.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the significance of the coefficients in a system of equations?

Back

Coefficients determine the slope and position of the lines represented by the equations.

Tags

CCSS.8.EE.C.8A