What are the solutions for the following system of equations?
y=8x+7
y=-x^2-5x+7
equate the two functions, since they are both y:
8x+7 = -x^2-5x+7
x^2+13x = 0
x(x+13) = 0
. . .
To find the solutions for the given system of equations, we need to find the values of x and y that satisfy both equations simultaneously.
Let's start by equating the two expressions for y and solving for x:
8x + 7 = -x^2 - 5x + 7
Rearranging the equation, we get:
x^2 + 13x = 0
Factoring out the common factor x, we have:
x(x + 13) = 0
Now we can set each factor equal to zero and solve for x:
x = 0 or x + 13 = 0
From the first equation, we find x = 0, and from the second equation, we get x = -13.
Now that we have the values of x, we can substitute them back into either equation to find the corresponding values of y.
For x = 0:
y = 8(0) + 7
y = 7
Therefore, one solution is (x, y) = (0, 7).
For x = -13:
y = 8(-13) + 7
y = -104 + 7
y = -97
Another solution is (x, y) = (-13, -97).
Hence, the system of equations has two solutions: (0, 7) and (-13, -97).