Question

Give two systems of equations that would be easier to solve by substitution than by elimination. Then give two systems that would be easier to solve with elimination. Finally, explain how you decide whether to use elimination or substitution to solve a system.

A) (1) 2x + 3y = 7, x - 2y = 4
(2) 3x - 4y = 5, 5x + 2y = 10
Elimination is easier when coefficients of one variable can be easily canceled out.
B) (1) 3x - y = 6, 2x + y = 5
(2) 4x + 2y = 10, x - 3y = 7
Substitution is easier when one equation can be easily solved for one variable.
C) (1) x - 2y = 5, 3x + 2y = 9
(2) 2x - 4y = 10, 4x + 3y = 15
Elimination is easier when the coefficients can be easily combined to eliminate a variable.
D) (1) 2x + 3y = 8, x - 4y = 7
(2) 5x - 2y = 3, 3x + y = 5
Substitution is easier when one equation can be solved for one variable.

Answer 1

Two systems of equations that are easier to solve by substitution and elimination, and how to decide which method to use.

Step-by-step explanation:

Two systems of equations that would be easier to solve by substitution than by elimination are:

A) (1) 2x + 3y = 7, x - 2y = 4 (2) 3x - 4y = 5, 5x + 2y = 10

B) (1) 3x - y = 6, 2x + y = 5 (2) 4x + 2y = 10, x - 3y = 7

Two systems of equations that would be easier to solve with elimination are:

C) (1) x - 2y = 5, 3x + 2y = 9 (2) 2x - 4y = 10, 4x + 3y = 15

D) (1) 2x + 3y = 8, x - 4y = 7 (2) 5x - 2y = 3, 3x + y = 5

The choice between elimination and substitution depends on the specific equations. Elimination is easier when coefficients of one variable can be easily canceled out, while substitution is easier when one equation can be easily solved for one variable.