what are the solutions to the system?
y=x^2 - 6x+7
y=-x+13
Would it be: (-1, 14) and (6,7)?
That would be correct.
I'm still pretty lost.. :/
ok, the next step is
(x-6)(x+1) = 0
x = 6 or -1
Now just find y for each of those x values.
thx guys
equate y and you have
x^2-6x+7 = -x+13
x^2-5x-6 = 0
and I think you can take it from there, yeah?
To find the solutions to the system of equations, we need to find the values of x and y that satisfy both equations simultaneously. Let's solve the system step by step:
Step 1: Set the two equations equal to each other:
x^2 - 6x + 7 = -x + 13
Step 2: Rearrange the equation to bring all the terms to one side:
x^2 - 6x + x - 7 - 13 = 0
Simplifying further:
x^2 - 5x - 6 = 0
Step 3: Now we have a quadratic equation. To solve it, we can factor or use the quadratic formula. Let's factor the quadratic equation:
(x - 6)(x + 1) = 0
Setting each factor equal to zero:
x - 6 = 0 or x + 1 = 0
Solving for x in each equation:
x = 6 or x = -1
Step 4: Substitute the values of x into either of the original equations to find the corresponding y-values.
Using the first equation:
y = (6)^2 - 6(6) + 7
y = 36 - 36 + 7
y = 7
Using the second equation:
y = -(-1) + 13
y = 1 + 13
y = 14
Therefore, the solution to the system of equations is:
(x, y) = (6, 7) and (-1, 14)