3x + 3y = 15
8x + 5y = 46
What is the solution to the system of equations above?
Responses
A x = -3, y = 6x = -3, y = 6
B x = 7, y = -2x = 7, y = -2
C x = 6, y = -4x = 6, y = -4
D x = -2, y = -6
To solve this system of equations, one method is to use the substitution method.
Starting with the first equation, 3x + 3y = 15, we can solve for x in terms of y:
3x = 15 - 3y
x = (15 - 3y)/3
x = 5 - y
Now we substitute this expression for x into the second equation, 8x + 5y = 46:
8(5 - y) + 5y = 46
40 - 8y + 5y = 46
-3y = 6
y = -2
Substituting this value of y back into the expression for x, we get:
x = 5 - (-2)
x = 5 + 2
x = 7
Therefore, the solution to the system of equations is x = 7, y = -2.
The correct response is: B. x = 7, y = -2
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)