Solving a System of Equations with Simple Substitution

Solve the following system of equations using the substitution method: x + 2y - z = 4 2x - y + 3z = 7 3x + y + 2z = 1

• The system of equations has infinitely many solutions.

• The system of equations has exactly one solution.

• The system of equations is dependent and has no unique solution.

• The system of equations is inconsistent and has no solution.

What is the substitution method used for in solving 3-variable systems?

• To solve for one variable and substitute it into the other equations.

• To graph the system of equations.

• To solve for all variables simultaneously.

• To find the determinant of the coefficient matrix.

When using the substitution method, what is the first step to substitute one variable?

• Multiply both sides of the equation by a constant.

• Solve one of the equations for one variable in terms of the other variable.

• Simplify the equation.

• Rearrange the equation to isolate one variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Which method is most suitable for solving 3-variable systems when the coefficients are simple and easy to work with?

• matrix method

• graphing method

• substitution method

• elimination method

What is the solution to this system? Solve by substitution.
y= 4x + 3
2x - 3y = 21

• (3,-9)

• (-3,-9)

• (-3,9)

• (0,1)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

solve by substitution: y=3x+14
y=-4x

• y=3

• y=1

• y= - 2

• y=4

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Solve the following systems of equations using substitution:

x = 5

2x + y = 10

• No solution

• (0, 5)

• (5, 10)

• (5, 0)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Solve the following systems of equations using substitution:

5x - 2y = 3

y = 2x

• (6, 3)

• (1, 2)

• (3, 6)

• (2, 1)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Solve the following systems of equations using substitution:

2y + x = -15

x = 3y

• (-3, -9)

• (-9, -3)

• (-3, 9)

• (9, -3)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Solve the following systems of equations using substitution:

y = 3 - x

3y + x = 5

• No solution

• (1, 2)

• (3, 0)

• (2, 1)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6