See solutions and explanations on solving simultaneous equations below.
Step-by-step explanation:
9. Given that Steve started with $300 and spent $50 per week where as Chelsea started with $0 and saved $50 per week, then the equations are;
Steve, y=300-50x
Chelsea , y= 0+50x
where x is the number of weeks
Solving the equations
y=300-50x------(i)
y=50x ------(ii)
using equation ii in i
50x=300-50x
50x+50x=300
100x=300
x=300/100 =3
y=150x ----y=50*3=150
(x,y)=(3,150)
At week 3, both Steve and Chelsea will have $150
Check the graph 1, for the solution
10.
If you add the two equations, the y variable will be eliminated
(i) 3x-4y=12
(ii) 3x+4y=8
adding the two equations
6x+0=20
6x=20
x=20/6
11. Given the equations as;
2y-2x= -8 -------(i)
y= -2x +5 ..........(ii)
Apply the substitution method as: use equation (ii) in (i)
2( -2x+5) -2x= -8
-4x+10-2x = -8
10-6x =-8
10+8= 6x
18 = 6x
18/6 = x
3=x
y= -2x+5
y=-2(3) +5
y=-6+5
y= -1
The solution is : x= 3, y= -1
12.
The slope of the graphs is the same. This means the system has infinite solution because the equations of the lines are basically the same.Here, the slope and the y-intercept values are the same.
13.
Form the linear equations in this case where n = a note book and p =pen
Samantha.... 5n+2p= 9
Jeffrey..........3n +2p =6
Apply subtraction to eliminate the variable p to remain with
2n=3
n=3/2 = 1.5
Use n=1.5 in the equation 5n+2p=9
5n+2p=9
5(1.5) +2p=9
7.5 +2p =9
2p=9-7.5
2p=1.5
p=1.5/2 =0.75
A notebook is $1.5 and a pen is $0.75
14.
Let an adult ticket to be =a
Let children ticket to be=c
For Garcia's family..... 2a+3c=$44.50
For Smith's family........ 3a+6c=$78
The equations formed are;
2a + 3c = 44.50
3a + 6c=78
Make the side with a variable equal by multiplying the equation as;
3 (2a +3c =44.50)
2( 3a+6c= 78)
This will form;
6a +9c = 133.5
6a + 12c=156
Apply subtraction to form
3c=22.5
c=22.5/3 = 7.5
Use value of c in 3a+6c=78 as
3a +6(7.5) = 78
3a+ 45=78
3a= 78-45
3a=33
a=33/3 = 11
Price of adult ticket is $11
Price of children ticket is $7.5
15.
The system of equations have infinitely many solutions. This is because the graphs are exactly the same line. When you graph a system of equations, the intersection of the line is the solution.If the graphs overlaps at every point, they are exactly the same line thus it means at any point of the line is a solution.
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Keywords :equations, system , solutions, infinite solution, slope
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