Step-by-step explanation:
<u>Given equation:</u>
a. write a second equation so that (1,3) is the only solution of the system
To have only one solution the equation must have a different slope.
<u>Let it be 10, then the y-intercept of y = 10x + b is:</u>
<u>And the equation:</u>
b. Write a second equation so that the system has infinitely many solutions
<u>To have infinitely many solutions, both equations must be same:</u>
c. Write a second equation so that the system has no solutions.
<u>To have no solutions, the equations must have same slope but different y-intercepts:</u>
It takes 7 hours to mow 4 lawns
Therefore every hour, (4 ÷ 7) or 4/7 lawns are mowed. This gives the rate.
For 35 hours, 4/7 x 35 lawns are mowed.
=35 ÷ 7 = 5
= 4 × 5
= 20 lawns
The equation seems to be
1
-------- = 5 ^ (x + 4)
25
In that case, this is the solution, stept by step:
1) factor 25: 25 = 5^2
1
=> ----------- = 5^(x + 4)
5^2
2) invert 5^2
=> 5^(-2) = 5^(x+4)
3) Given that the bases are equal, the exponents also have to be equal:
=> - 2 = x + 4
3) transpose +4:
=> - 2 - 4 = x
=> x = - 6
Answer: - 6
