Solve the system equations
y=4x+8,x^2+7x-20
I'm truly lost
I assume your two equations are
y = 4x+8
y = x^2+7x-20
So, just set them equal:
x^2+7x-20 = 4x+8
x^2+3x-28 = 0
(x+7)(x-4) = 0
x = -7 or 4
See
http://www.wolframalpha.com/input/?i=x%5E2%2B7x-20+%3D+4x%2B8
Well, if you're lost, it's good to know that you're not alone. Being lost is just your internal GPS's way of saying, "Go on an adventure!" So, let's embark on this mathematical adventure together and solve the system of equations.
First, let's rearrange the first equation to solve for x:
y = 4x + 8
Now, let's substitute this expression for y into the second equation:
x^2 + 7x - 20 = 4x + 8
Next, let's simplify the equation by moving all the terms to one side:
x^2 + 7x - 4x - 20 - 8 = 0
Combining like terms gives us:
x^2 + 3x - 28 = 0
Now, we can factor the quadratic equation:
(x + 7)(x - 4) = 0
Setting each factor equal to zero, we find that x = -7 and x = 4.
So, the solutions to the system of equations are x = -7 and x = 4.
Now, if you're still feeling lost, don't worry! It's just a temporary confusion before finding the right path. Embrace the adventure, and soon enough, you'll find your way.
To solve the system of equations, we will use substitution method.
Step 1: Start with the first equation:
y = 4x + 8 ............(1)
Step 2: Substitute this value of y in the second equation:
x^2 + 7x - 20 = 4x + 8 ............(2)
Step 3: Rearrange the equation by moving all variables to one side:
x^2 + 7x - 4x - 20 - 8 = 0
x^2 + 3x - 28 = 0
Step 4: Solve the quadratic equation by factoring or using the quadratic formula. Let's use factoring here:
The equation can be factored as: (x - 4)(x + 7) = 0
So, either (x - 4) = 0 or (x + 7) = 0
Step 5: Solve for x:
If (x - 4) = 0, then x = 4
If (x + 7) = 0, then x = -7
Step 6: Substitute the values of x back into the original equation to find the corresponding y-values:
For x = 4:
y = 4x + 8
y = 4(4) + 8
y = 16 + 8
y = 24
For x = -7:
y = 4x + 8
y = 4(-7) + 8
y = -28 + 8
y = -20
Step 7: The solutions to the system of equations are:
(x, y) = (4, 24) and (-7, -20)
To solve the system of equations, we need to find the values of x and y that satisfy both equations simultaneously. Let's go step by step.
First, let's solve the second equation: x^2 + 7x - 20 = 0. This is a quadratic equation, so we can solve it by factoring or by using the quadratic formula. Let's factor it:
(x + 10)(x - 2) = 0
Now, we have two possible solutions for x: x + 10 = 0 or x - 2 = 0.
If x + 10 = 0, then x = -10.
If x - 2 = 0, then x = 2.
So the possible values for x are -10 and 2.
Now, let's substitute these values of x into the first equation, y = 4x + 8, to find the corresponding values of y.
For x = -10:
y = 4(-10) + 8
y = -40 + 8
y = -32
So we have one solution: x = -10 and y = -32.
For x = 2:
y = 4(2) + 8
y = 8 + 8
y = 16
So we have another solution: x = 2 and y = 16.
Therefore, the system of equations has two solutions:
(x, y) = (-10, -32) and (2, 16).