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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 + 14 3y + 14
B 3y − 14 3y − 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)

1 Answer

1 vote

Final answer:

To solve this linear system by substitution, the expression -3y + 14 could be substituted for x. The solution to the system of equations is the ordered pair (2, 4).

Step-by-step explanation:

To solve this linear system by substitution, we need to choose an expression that represents x in terms of y or vice versa. Looking at the given equations, we see that the second equation, x + 3y = 14, can be rearranged to solve for x: x = 14 - 3y. Therefore, expression C (-3y + 14) could be substituted for x.

To find the solution to the system of equations, we need to substitute the expression for x into the first equation and solve for y. Substituting -3y + 14 for x in the first equation, 3(-3y + 14) - 2y = -2. Simplifying this equation, we get -9y + 42 - 2y = -2. Combining like terms, we have -11y + 42 = -2. Solving for y, we subtract 42 from both sides to get -11y = -44. Dividing both sides by -11, we find y = 4.

Now that we have the value of y, we can substitute it back into one of the original equations to find the value of x. Using the second equation, x + 3(4) = 14. Simplifying, we get x + 12 = 14. Subtracting 12 from both sides, x = 2. Therefore, the solution to the system of equations is ordered pair A (2, 4).

User Alaa Sadik
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