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)
Question 1:
To solve the system by substitution, we need to eliminate one variable by expressing it in terms of the other variable. In this case, we can rearrange the second equation to solve for x: x = 14 - 3y.
Therefore, the expression that could be substituted for x is: 14 - 3y.
Answer: A) 3y + 14
Question 2:
To find the ordered pair solution, we substitute the x-value and y-value into either of the original equations and solve for both variables. Let's use the first equation:
3x - 2y = -2
Substituting x = 14 - 3y:
3(14 - 3y) - 2y = -2
42 - 9y - 2y = -2
42 - 11y = -2
-11y = -44
y = 4
Substituting y = 4 back into x = 14 - 3y:
x = 14 - 3(4)
x = 14 - 12
x = 2
Therefore, the ordered pair solution is (2, 4).
Answer: A) (2, 4)