Simple Solving Systems of Equations by Substitution

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.

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.

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)

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

• y=3

• y=1

• y= - 2

• y=4

Solve the system of equations.

y = -5x

x + 3y = 28

• (-6, 30)

• (-2, 10)

• (-2, 39)

• No solution

• Infinite solutions

x = -3y - 17

2x + 3y = -7

• (1, -20)

• (10, 0)

• (-5, -2)

• (10 , -9)

3x + 2y = 8

-x + y = -11

• (-5,6)

• (6,-11)

• (-6,-5)

• (6,-5)

What is the solution to the system of equations?

• (3,1)

• (1,3)

• (3,-1)

• (3,-1)