9. Find the solutions to the system.
y=x^2+5x+6
y=4x+12
A. (2,20) and (-3,0)
B. (2,20) and (-3,-18)
C. (-2,-20) and (-3,-18)
D. no solutions
10. Find the solutions to the system.
y=x^2-3x-1
y=8x-1
A. (0,-1) and (11,388)
B. (0,-1) and (11,87)
C. (-1,0) and (87,11)
D. no solutions
I'm in Connections academy if that helps get me the right answers lol
Answers for the other questions would be appreciated if you have it!
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To find the solutions to the given systems of equations, you need to solve the equations simultaneously. You can do this by setting the two expressions for "y" equal to each other and solving for "x". Once you find the value(s) of "x", you can substitute it back into either equation to solve for the corresponding "y" value(s). Let's solve each system step by step:
9. Given system:
y = x^2 + 5x + 6 ...(Equation 1)
y = 4x + 12 ...(Equation 2)
Setting Equation 1 and Equation 2 equal to each other:
x^2 + 5x + 6 = 4x + 12
Rearranging this equation:
x^2 + 5x - 4x + 6 - 12 = 0
x^2 + x - 6 = 0
Now, we can factorize or use the quadratic formula to solve for "x". Factoring the quadratic equation gives us:
(x + 3)(x - 2) = 0
Setting each factor to zero and solving for "x":
x + 3 = 0 -> x = -3
x - 2 = 0 -> x = 2
Now substitute the values of "x" back into either Equation 1 or Equation 2 to solve for "y".
Using Equation 1:
y = (-3)^2 + 5(-3) + 6 -> y = 9 - 15 + 6 -> y = 0
Using Equation 2:
y = 4(2) + 12 -> y = 8 + 12 -> y = 20
Therefore, the solutions to the system are (x, y) = (-3, 0) and (2, 20).
So the correct answer is A. (2, 20) and (-3, 0).
10. Given system:
y = x^2 - 3x - 1 ...(Equation 1)
y = 8x - 1 ...(Equation 2)
Setting Equation 1 and Equation 2 equal to each other:
x^2 - 3x - 1 = 8x - 1
Rearranging this equation:
x^2 - 3x - 8x - 1 + 1 = 0
x^2 - 11x = 0
Factoring out "x":
x(x - 11) = 0
Setting each factor to zero and solving for "x":
x = 0
x - 11 = 0 -> x = 11
Now substitute the values of "x" back into either Equation 1 or Equation 2 to solve for "y".
Using Equation 1:
y = (0)^2 - 3(0) - 1 -> y = 0 - 0 - 1 -> y = -1
Using Equation 2:
y = 8(11) - 1 -> y = 88 - 1 -> y = 87
Therefore, the solutions to the system are (x, y) = (0, -1) and (11, 87).
So the correct answer is B. (0, -1) and (11, 87).
I hope this clears your doubts! Let me know if you need further assistance.
Your school doesn't influence the right answers.
By the way -- what are the right answers? We'll be glad to check your answers.