Answer:
1. (7.4,3.6)
2. (3,-1)
3. (-2,-3)
4. Infinite number of solutions.
Step-by-step explanation:
We can solve systems of equations 3 ways: graphing, substitution, and elimination. We will solve 1-2, 4 using substitution and 3 with elimination.
1. Since x=4y-7, we substitute it in for x . It's better than elimination because of how it is set-up unless there is a typo.
- So -4x+4y=-8 becomes -4(4y-7)+4y=-8.
- We simplify to -14y+28+4y=-8.
- We add like terms to get -10y+28=-8.
- We now solve for y by subtracting 28 and dividing by -10.
- -10y+28-28=-8-28
- -10y=-36
- y=3.6
- We substitute y=3.6 into x=4y-7. x=4(3.6)-7=14.4-7=7.4
2. Since none of the coefficients of x & y are the same, we will rearrange and substitute.
- -8x+2y=-26 becomes 2y=8x-26 by adding 8x to both side.
- We divide by 2. y=4x-13.
- We substitute into -5x-5y=-10. -5x-5(4x-13)=-10
- We simplify to -5x-20x+65=-10
- We add like terms. -25x+65=-10
- We now solve for x by subtracting 65 and dividing by -25.
- -25x+65-65=-10-65
- -25x=-75
- x=3
- We substitute x=3 into -8(3)+2y=-26
- -24+2y=-26
- 2y=-2
- y=-1
3. We can solve this system through elimination. We subtract or add the equations when the coefficients are the same to eliminate one variable.
- We susbstitute y=-3 into one of the equations 3x-(-3)=-3.
- 3x=-6
- x=-2
4. Since none of the coefficients of x & y are the same, we will rearrange and substitute.
- -x+y=-2 becomes y=x-2
- We substitute into 4x-4(x-2)=8.
- Simplify 4x-4x+8=8.
- Add like terms 0x+8=8
- 8=8
- This is a true statement and a special solution. It means infinite number of solutions.
By using the concept and properties of percentages, we conclude that the hospital has a total of 300 beds.
<h3>How many beds are available in a hospital?</h3>
In accordance with the statement, there are 210 patients in the beds of a hospital and 30 % of the beds are available. We must take advantage of the concept of percentage to calculate the total number of beds. 210 patients occupy 70 % of the beds.
Then, the total number of beds at the hospital is determined by dividing the number of beds with patients and its respective percentage:
n = 210 / 70 %
n = 210 / (70 / 100)
n = (210 · 100) / 70
n = 300
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Partial Answer:
For #10 the solutions are 2 and 5
Step-by-step explanation:
Solutions for an equation can be x-intercepts, or where it touches the x or horizontal line. The equation in #10 touches the x line at 2 and 5.
The estimated population, if the rate is a growth rate is 34696 populations
The estimated population, if the rate is a decline rate is 5657 populations
<h3> Exponential functions</h3>
The standard exponential equation is expressed as 
where;
- a is the intercept
- b is the growth rate
- x is the time taken
If the initial population is 15,000 with a rate of 15%, then;
a) If the rate is a growth rate, the estimated population will be expressed as;
The estimated population, if the rate is a decline rate is 34696 populations
b) If the rate is a decline rate, the estimated population will be expressed as;
The estimated population, if the rate is a decline rate is 5657 populations
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