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: The expression that could be substituted for x is B) 3y - 14.
Question 2: The ordered pair that is the solution to the system is B) (2, -4).
Solve the system of equations using any method.
y = -3x + 5 and y = 6x + 2
Responses
A (3, 3)(3, 3)
B (-3, 1)(-3, 1)
C (-3, -1)(-3, -1)
D (1/3, 4)
To solve the system of equations, we can set the two expressions for y equal to each other and solve for x.
-3x + 5 = 6x + 2
To solve for x, we will isolate it on one side of the equation by subtracting 6x from both sides and adding 5 to both sides:
-3x - 6x = 2 - 5
-9x = -3
x = (-3)/(-9)
x = 1/3
Now that we have the value of x, we can substitute it back into either of the original equations to solve for y.
Let's use the first equation:
y = -3(1/3) + 5
y = -1 + 5
y = 4
Therefore, the solution to the system of equations is (1/3, 4), which corresponds to option D).