Solve Linear System by Substitution
Consider this linear system:
3x − 2y = −2
x + 3y = 14
Question 1
To solve this system by substitution, which expression could be substituted for x?
Responses
A 3y + 143y + 14
B 3y − 143y − 14
C −3y + 14−3y + 14
D −3y − 14−3y − 14
Question 2
Which ordered pair is the solution to the system?
Responses
A (2, 4)(2, 4)
B (2, −4)(2, −4)
C (−2, 4)(−2, 4)
D (−2, −4)(−2, −4)
Question 1:
To solve the system by substitution, we need to express one variable in terms of the other and then substitute that expression into the other equation. We can rearrange the second equation x + 3y = 14 to solve for x:
x = 14 - 3y
Therefore, the expression that could be substituted for x is C) -3y + 14.
Question 2:
To find the solution to the system, we substitute the expression for x into the first equation 3x - 2y = -2:
3(14 - 3y) - 2y = -2
42 - 9y - 2y = -2
42 - 11y = -2
-11y = -44
y = 4
Plugging this value back into the second equation, we find:
x + 3(4) = 14
x + 12 = 14
x = 2
Therefore, the solution to the system is A) (2, 4).