Question 75561This question is from textbook Beginning Algebra
: Please help!!! I don't understand any of this. Any assistance you can provide will be greatly appreciated. Thanks in advance.
PG. 483
Find the solution to each system of equations by the substitution method. Check your answers. Place your solution in the form (x,y), (a,b), (p,q), or (s,t).
(2.) x = 4 - 4y (6.) 4x + 2y = 4
-x + 2y = 2 3x + y = 4
PG. 490
Find the solution by the addition method. Check your answers.
(6.) -x + y = 2 (8.) 2x + y = 4 (14.) 5x - 3y = 14
x + y = 4 3x - 2y = -1 2x - y = 6
PG. 504
Solve using two equations with two variables.
(4.) El Segundo High School put on their annual musical. The students sold 650 tickets for a value of $4375. If orchestra seats cost $7.50 and balcony seats cost $3.50, how many of each kind of seats were sold?
This question is from textbook Beginning Algebra
Answer by funmath(2933)   (Show Source):
You can put this solution on YOUR website! PG. 483
Find the solution to each system of equations by the substitution method. Check your answers. Place your solution in the form (x,y), (a,b), (p,q), or (s,t).
(2.) x = 4 - 4y
-x + 2y = 2
Substitute x=4-4y in the second equation and solve for y:
-(4-4y)+2y=2
-4+4y+2y=2
-4+6y=2
4-4+6y=2+4
6y=6
6y/6=6/6
y=1
Now substitute y=1 in the first equation and solve for x.
x=4-4(1)
x=4-4
x=0
The solution is (x,y)=(0,1)
You check by substituting x=0 and y=1 into both equations and see if they balance:
0=4-4(1)
0=4-4
0=0 the first one checks
-(0)+2(1)=2
0+2=2
2=2 The second one checks as well, so you're right.
:
(6.) 4x + 2y = 4
3x + y = 4
Solve the second equation for y.
3x-3x+y=4-3x
y=4-3x
Now substitute y=4-3x into the first equation and solve for x.
4x+2(4-3x)=4
4x+8-6x=4
-2x+8=4
-2x+8-8=4-8
-2x=-4
-2x/-2=-4/-2
x=2
Now substitute x=2 into the second equation and solve for y.
3(2)+y=4
6+y=4
6-6+y=4-6
y=-2
The solution is (x,y)=(2,-2)
Check by substituting x=2 and y=-2 in both equations and see if they balance.
4(2)+2(-2)=4
8-4=4
4=4 First equation checks out.
3(2)+(-2)=4
6-2=4
4=4 This one checks too.
:
Find the solution by the addition method. Check your answers.
(6.) -x + y = 2 Add the two equations together and the x's are eliminated
x + y = 4
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0+2y=6 solve for y
2y=6
2y/2=6/2
y=3
Substitute y=3 into either equation and solve for x.
x+(3)=4
x+3-3=4-3
x=1
The solution is (x,y)=(1,3) I'll leave the rest for you to check.
(8.) 2x + y = 4
3x - 2y = -1
If you multiply the first equation by 2 the y's will be eliminated when you add the equations. 2(2x+y)=2(4)--->4x+2y=8
4x+2y=8
3x-2y=-1
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7x+0=7 solve for x
7x=7
7x/7=7/7
x=1
Substitute x=1 into either equation and solve for y.
2(1)+y=4
2+y=4
2-2+y=4-2
y=2
The solution is (x,y)=(1,2) Don't forget to check it.
:
(14.) 5x - 3y = 14
2x - y = 6
Multiply the second equation by -3 and the y's will be eliminated when you add the equations. -3(2x-y)=-3(6)---->-6x+3y=-18
5x-3y=14
-6x+3y=-18
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-x+0=-4
-x/-1=-4/-1
x=4
Substitute that into either equation:
2(4)-y=6
8-y=6
8-8-y=6-8
-y=-2
-y/-1=-2/-1
y=2
The solution is (x,y)=(4,2) Don't forget to check it.
:
PG. 504
Solve using two equations with two variables.
(4.) El Segundo High School put on their annual musical. The students sold 650 tickets for a value of $4375. If orchestra seats cost $7.50 and balcony seats cost $3.50, how many of each kind of seats were sold?
Let orchestra seats be: x
Let balcony seats be: y
Then the amount of tickets sold is represented by: x+y=650
The amount of money made on the tickets is: 7.50x+3.50y=4375
You can use either substitution or elimination to solve, I think in this case, substitution is easiest.
x+y=650
x-x+y=650-x
y=650-x substitute into the second equation.
7.50x+3.50(650-x)=4375
10(7.50x)+10(3.50)(650-x)=10(4375)
75x+35(650-x)=43750
75x+22750-35x=43750
40x+22750=43750
40x+22750-22750=43750-22750
40x=21000
40x/40=21000/40
x=525
Substitute that into the first equation
525+y=650
525-525+y=650-525
y=125
Orchestra seats x=525
Balcony seats y=125
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Happy Calculating!!!!
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