5.Regarding the equations below. What is the value of x? 5x + 2y = 4 x – 3y = –23
1 answer:
Answer:
x=−2
y=7
Step-by-step explanation:
5x+2y=4
x−3y=−23
In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.
5x+2y=4,x−3y=−23
To make 5x and x equal, multiply all terms on each side of the first equation by 1 and all terms on each side of the second by 5.
5x+2y=4,5x+5(−3)y=5(−23)
Simplify.
5x+2y=4,5x−15y=−115
Subtract 5x−15y=−115 from 5x+2y=4 by subtracting like terms on each side of the equal sign.
5x−5x+2y+15y=4+115
Add 5x to −5x. Terms 5x and −5x cancel out, leaving an equation with only one variable that can be solved.
2y+15y=4+115
Add 2y to 15y.
17y=4+115
Add 4 to 115.
17y=119
Divide both sides by 17.
y=7
Substitute 7 for y in x−3y=−23. Because the resulting equation contains only one variable, you can solve for x directly.
x−3×7=−23
Multiply −3 times 7.
x−21=−23
Add 21 to both sides of the equation.
x=−2
The system is now solved.
x=−2,y=7
Graph if needed:
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Answer:
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Step-by-step explanation:
x = number of dimes
y = number of quarters
minimum is greater than or equal to ≥
x+y ≥16
no more than is less than or equal to ≤ ,
value of dime is $ 0.10
value of quarter is $0.25 so
0.10x + 0.25y ≤ 3.00
Rewrite inequalities in terms of y:
y ≥16 - x
(0.25/0.25)y ≤ (3.00/0.25)-(0.10/0.25)x→
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Graph system: see file
Answer:
2 weeks
Step-by-step explanation:
y = mx + b
y = total number of chapters read =
m = number of chapters read per week =
x = number of weeks = what we're solving for
b is not needed to find this solution
=
x divide
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Answer:
(a)Charlie is right
(b)$0
Step-by-step explanation:
(a)A game is said to be a fair game when the probability of winning is equal to the probability of losing. Mathematically, a game is said to be fair when the expected value is zero.
In the game, the possible outcomes are: HH, HT, TH and TT.
Charlie wins when the outcome is HH, TT
- P(Charlie Wins)=2/4
- P(Charlie Losses)=2/4
Lucy wins when the outcome is HT or TH
- P(Lucy Wins)=2/4
- P(Lucy Losses)=2/4
Therefore, the game is fair. Charlie is right.
(b)
If the outcome is HH, Lucy pays $3.
If the outcome is HT or TH, Lucy gets $2.
If the outcome is TT, Lucy pays $1.
The probability distribution of Lucy's profit is given below:
Expected Profit
Lucy's expected profit from the game is $0.