find the solutions to the system
y= x^2 + 8x +2
y= 7x +4
A (-2,-10) and (1,11)
B (2,10) and (-1,-11) my answer
C (-2, -34) and (1,11)
D No solutions.
y= x^2 + 8x +2.....(*)
y= 7x +4.......(**)
----------------------------
Equating *&**
x²+8x+2=7x+4
x²+x-2=0
Factored as
(x-1)(x+2)=0
x=1or -2
Insert those values into
Y=7x+4
to find y respectively
Hmmm none of my x value suit the options
since y = 7x+4,
x^2 + 8x + 2 = 7x + 4
Now just solve for x as usual, and then y = 7x+4
Forget about my last statement.....did scan through the options properly
x=1
y=11
To find the solutions to the system of equations, you need to solve the equations simultaneously. The given equations are:
y = x^2 + 8x + 2 --- Equation 1
y = 7x + 4 --- Equation 2
To solve the system, you can substitute the value of y from Equation 2 into Equation 1. This gives:
7x + 4 = x^2 + 8x + 2
Rearrange the equation to get all terms on one side:
x^2 + 8x - 7x + 2 - 4 = 0
Simplify the equation:
x^2 + x - 2 = 0
Now you can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. The quadratic equation factors as:
(x + 2)(x - 1) = 0
So the solutions for x are x = -2 and x = 1.
Now substitute these values back into either of the original equations to find the corresponding y-values. Let's use Equation 2:
For x = -2:
y = 7(-2) + 4
y = -14 + 4
y = -10
So one solution is (-2, -10).
For x = 1:
y = 7(1) + 4
y = 7 + 4
y = 11
So another solution is (1, 11).
Therefore, the correct answer is A: (-2, -10) and (1, 11).