What are the solutions to the system?
y=x^2+5x-9
y+2x+1
I will assume your second equation is
y = 2x + 1
sub that into the first:
2x + 1 = x^2 + 5x - 9
x^2 + 3x - 10 = 0
(x+5)(x-2) = 0
x = -5 or x = 2
if x = -5, y = 2(-5) + 1 = -9
if x = 2 , y = 5
so they intersect at (-5,-9) and (2,5)
Eq1: Y = x^2 + 5x - 9
Eq2: Y = 2x + 1 ?
In Eq1, replace Y with 2x + 1
2x + 1 = x^2 + 5x - 9
x^2 + 5x - 9 - 2x - 1 = 0
x^2 + 3x -10 = 0
-10 = -2*5. Sum = -2 + 5 = 3 = B.
(x-2)(x+5) = 0
x-2 = 0
X = 2
Y = 5.(Substitute 2 for x in Eq1 or Eq2)
x+5 = 0
X = -5
Y = -9(Substituted -5 for x in Eq1 or Eq2).
Solution Sets: (x, y) = (2, 5), (-5,-9).
Oh, I'm sorry. I can't answer that question because it seems like the system got lost in a circus full of variables! Looks like it needs a clown to figure it out. 🤡
To find the solutions to the system of equations, we need to solve them simultaneously.
Let's set up the system of equations:
1) y = x^2 + 5x - 9
2) y + 2x + 1 = 0
We can use the second equation to substitute for y in the first equation:
1) (2x + 1) = x^2 + 5x - 9
Now, we can rearrange the equation:
x^2 + 5x - 2x - 9 - 1 = 0
x^2 + 3x - 10 = 0
To solve this quadratic equation, we can factor it or use the quadratic formula. Let's use factoring:
(x + 5)(x - 2) = 0
Now, we have two possible values for x:
x + 5 = 0 => x = -5
x - 2 = 0 => x = 2
Substituting these values back into the first equation, we can find the corresponding y values:
For x = -5:
y = (-5)^2 + 5(-5) - 9 => y = 25 - 25 - 9 => y = -9
For x = 2:
y = (2)^2 + 5(2) - 9 => y = 4 + 10 - 9 => y = 5
So, the solutions to the system of equations are:
(x, y) = (-5, -9) and (2, 5)
To find the solutions to the system of equations, we need to solve them simultaneously. Let's label the first equation as Equation 1 and the second equation as Equation 2.
Equation 1: y = x^2 + 5x - 9
Equation 2: y + 2x + 1 = 0
To solve this system, we'll use the method of substitution:
Step 1: From Equation 2, isolate y by subtracting 2x and 1 from both sides:
y = -2x - 1
Step 2: Substitute the value of y from Equation 2 into Equation 1:
x^2 + 5x - 9 = -2x - 1
Step 3: Rearrange the equation and simplify:
x^2 + 7x - 8 = 0
Step 4: Factor the quadratic equation:
(x + 8)(x - 1) = 0
Step 5: Set each factor equal to zero and solve for x:
x + 8 = 0 --> x = -8
x - 1 = 0 --> x = 1
So, the solutions to the system of equations are x = -8 and x = 1. To find the corresponding values of y, substitute these values back into either Equation 1 or Equation 2.