Solve
k^2 + km = 8
m = k- 6
Can you show me step-by step please?
substitute m from the second equation into the first to give:
k² + k(k-6) = 8
k² + k² - 6k = 8
2k² -6k -8 =0
k² -3k -4 = 0
(k-4)(k+1)=0
k=4 or k=-1
Substitute each value of k into the second equation to give:
m=k-6
=4-6
=-2
or
m=k-6
=-1-6
=-7
Of course! Let's solve the equations step-by-step.
First, we will substitute the value of m from the second equation into the first equation.
Given: m = k - 6
Substituting this value into the first equation:
k^2 + k(k - 6) = 8
Next, distribute k to the terms inside the parentheses:
k^2 + k^2 - 6k = 8
Combine like terms:
2k^2 - 6k = 8
Now, rearrange the equation in standard quadratic form:
2k^2 - 6k - 8 = 0
To solve this quadratic equation, we can use factoring, completing the square, or using the quadratic formula. Let's use factoring in this case.
First, let's factor out the greatest common factor, which is 2:
2(k^2 - 3k - 4) = 0
Next, we can factor the quadratic expression inside the parentheses:
2(k - 4)(k + 1) = 0
Now, we can set each factor equal to zero and solve for k:
k - 4 = 0 or k + 1 = 0
Solving each equation separately:
k = 4 or k = -1
Now that we have the possible values for k, we can substitute them back into the second equation to find the corresponding values of m.
For k = 4:
m = k - 6 = 4 - 6 = -2
For k = -1:
m = k - 6 = -1 - 6 = -7
Therefore, the solution to the system of equations is:
k = 4, m = -2
k = -1, m = -7