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
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
Hi I'm just very very confused here! I've tried and I just can't figure it out.
what are the answers
9
A. (2,20) and (-3,0)
10
b. (0, -1) and (11, 87)
Hello I just figured them out! the first one is B and the second is A!
What have you done?
Did you set the y of one equation equal to the y of the other?
For the 2nd that is, x^2-3x-1 = 8x-1
x^2 - 11x = 0
did you factor this to x(x-11) = 0 ???
Now the answers are obvious
both are incorrect
Sub in your choices into the easy second equations, does not work!
To find the solutions to the given system of equations, we need to find the values of x and y that satisfy both equations simultaneously. Let's solve each system step by step:
1. System 1:
y = x^2 + 5x + 6
y = 4x + 12
To find the solutions, we'll set the two equations equal to each other:
x^2 + 5x + 6 = 4x + 12
Next, we'll rearrange the equation to bring all terms to one side:
x^2 + 5x - 4x + 6 - 12 = 0
Combining like terms:
x^2 + x - 6 = 0
Now, we can factor or use the quadratic formula to solve for x. In this case, the quadratic can be factored as:
(x - 2)(x + 3) = 0
So, either (x - 2) = 0 or (x + 3) = 0.
Solving these equations, we get:
x - 2 = 0 → x = 2
x + 3 = 0 → x = -3
Now, substitute these values of x back into one of the original equations to find the corresponding y-values:
For x = 2: y = (2)^2 + 5(2) + 6 = 20
For x = -3: y = (-3)^2 + 5(-3) + 6 = 0
Therefore, the solutions to the first system are (2, 20) and (-3, 0).
2. System 2:
y = x^2 - 3x - 1
y = 8x - 1
Again, we equate the two equations:
x^2 - 3x - 1 = 8x - 1
Rearranging the terms:
x^2 - 11x = 0
Factoring gives:
x(x - 11) = 0
So, either x = 0 or x - 11 = 0.
Solving for x, we have:
x = 0 or x = 11
Substituting these values into either of the original equations, we can find the corresponding y-values:
For x = 0: y = (0)^2 - 3(0) - 1 = -1
For x = 11: y = (11)^2 - 3(11) - 1 = 87
Thus, the solutions to the second system are (0, -1) and (11, 87).
From the answer choices given, it is clear that the correct answers are:
For the first system: Option A, (2, 20) and (-3, 0)
For the second system: Option B, (0, -1) and (11, 87)
I hope this helps you in understanding the process of solving systems of equations. Remember, always start by equating the two equations and then solving for the variables.