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Systems of Equations

Problems

Systems of Equations

Solving Systems of Linear Equations by Substitution

Problem : Which ordered pair(s) in the set {(7, 5),(5, 7),(13, 11),(- 2, 17)} satisfy the following system of equations?

10x + 7y = 99  
y - x = 2  

{(5, 7)}

Problem : Which ordered pair(s) in the set {(2, 5),(2, -9),(5, 2),(- 5, -2),(- 5, 12)} satisfy the following system of equations?

x + y = 7  
x 2 + 3x = 10  

{(2, 5),(- 5, 12)}

Problem : Solve by graphing:

y - 3x = -3  
y - 4 = - (x + 2)  


(x, y) = (2, 3)

Problem : Solve by graphing:

y = - x + 2  
y + 1 = 4(x + 3)  


(x, y) = (- 2, 3)

Problem : Is the following system consistent or inconsistent? Dependent or independent?

2x + 4y = 7  
x + 2y = 7  

Inconsistent, independent.

Problem : Is the following system consistent or inconsistent? Dependent or independent?

y = - x + 9  
y = - x + 9  

Consistent, independent.

Problem : Is the following system consistent or inconsistent? Dependent or independent?

3x - 7y = 6  
9x - 21y = 18  

Consistent, dependent.

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