Download Use substitution method to solve each system of equations. 15. Plug

Use substitution method to solve each system of equations.
15.
x  y  10
y  4x
Plug the second into the first:
 x + 4x = 10
5x = 10
X=2
Get y:
Y = 4x = 4*2 = 8
X = 2, y = 8
17.
4x y  9
2x  3y  27
Add y to the first one:
 y+9 = 4x
y = 4x-9
Plug that into the other one:
2x + 3(4x-9) = -27
2x + 12x – 27 = -27
14x = 0
X=0
Y = 4*0 – 9 = -9
X = 0, y = -9
1
3
1
x y
2
4
4
19.
 21.
x
4
y 
3
3

2x  y  1
23.
y  2x
Plug the second into the first:
 2x – (-2x) = -1
2x + 2x = -1
4x = -1
X = -1/4
Y = -2x = -2*-1/4 = ½
X = -1/4, y = 1/2
Use the elimination method to solve each system of equations.
27.
2x  4y  0
x  2y  5
Multiply the second one by 2:
 2x + 4y = 10
Add that to the first one:
4x = 10
X = 10/4 = 5/2
Get y:
X + 2y = 5
5/2 + 2y = 5
2y = 5/2
y = 5/4
So:
X = 5/2, y = 5/4
29.
5x  2y  1
x  3y  7
Multiply the second one by -5:
 -5x+15y = -35
Add that to the first one:
17y = -34
Y = -2
Get x:
X – 3(-2) = 7
X+6=7
X=1
So:
X = 1, y = -2
31.
5x  2y  27
3x  5y  18
Multiply the first one by 5 and the second one by 2:
 25x-10y=135
-6x+10y=36
Add them:
19x = 171
X=9
Get y:
-3(9) + 5y = 18
-27 + 5y = 18
5y = 45
Y=9
So:
X = 9, y = 9
33.
3x  5y  11
2x  6y  2
Multiply the first by 2 and the second by -3:
 6x – 10y = 22
-6x + 18y = -6
Add them:
8y = 16
Y=2
Get x:
2x – 6(2) = 2
2x – 12 = 2
2x = 14
X=7
So:
X = 7, y = 2
35.
x  2y  4
2x  4y  4
Multiply the first by -2:
 -2x + 4y = -8
Add to the second:
0 = -4
Not true, so NO solution
39.
x  3y  2
5x 15y  0
Rearrange the first one
 x-3y = -2
Multiply that by -5:
-5x + 15y = 10
Add that to the second equation:
0 = 10
Not true, so NO solution
41.
4 x  2y  5
2x  y  1
Multiply the second by -2:
 -4x – 2y = 2
Add that to the first:
0=7
Not true, so NO solution
43.
3
5
x  y  11
4
2
1
3
x  y  1
16
4
Clear the fractions:
 3x + 10y = 44
x-12y = -16
Multiply the second by -3:
-3x+36y = 48
Add to the other one:
46y = 92
Y=2
Get x:
x-12(2) = -16
x-24 = -16
x=8
So:
X = 8, y = 2
1. One number is two more than a second number. Twice the first is 4 less than
3 times the second. Find the numbers.
x = 2+y
2x = 3y – 4
Substitute:
2(2+y) = 3y-4
4 + 2y = 3y – 4
8 = y, x = 2+y = 10
The numbers are 10 and 8.
2. The USA has the worlds only large deck aircraft carriers, which can hold up
to 72 aircraft. The enterprise class carrier is longest in length while the
Nimitz class carrier is second longest. The total length of these two
carriers is 2193 feet while the difference of their lengths is only 9 feet.
A. Find the length of each class carrier
x+y=2193
x-y=9
Add them:
2x = 2202
Divide by 2:
X = 1101
So, y = 2193-1101 = 1092
They are: 1101 ft and 1092 ft
B. If a football field has a length of 100 yards, determine the length of
the Enterprise class carrier in terms of number of football fields.
1101 ft = 367 yards, between 3 and 4 football fields long (3.67 fields)
7.
Find how many quarts of a 4% butterfat milk and 1% butterfat milk should
be mixed to yield 60 quarts of 2 % butterfat milk.
0.04x + 0.01y = 60*0.02 = 1.2
x+y = 60
y = 60-x
Plug that in:
0.04x + 0.01(60-x) = 1.2
0.04x + 0.6 – 0.01x = 1.2
0.03x = 0.6
X = 20
So y = 60-x = 60-20 = 40
4% = 20
1% = 40
9.
In a recent year, the United Kingdom was the most popular host country for
US students traveling abroad to study. Spain was the second most popular
destination. A total of 40,012 students visited one of the two countries. If 15,428
more US students studied in the United Kingdom than in spain, find how many
students studied abroad in each country.
X+y=40012
x-y=15428
Add them:
2x = 55440
x = 27720
y = 40012-27720 = 12292
UK = 27720
Spain = 12292
11.
Karen Karlin bought some large frames for 15$ each and some small frames
for 8$ each at a sale. If she bought 22 frames for 239$ find how many of each type
she bought.
x+y=22
15x+8y=239
y = 22-x
15x + 8(22-x) = 239
15x + 176 – 8x = 239
7x = 63
X=9
Y = 22-9 = 13
So: 13 small, 9 large
13.
One number is two less than a second number, twice the first is 4 more than
3 times the second. Find the numbers.
X = y-2
2x = 4 + 3y
Substitute:
2(y-2) = 4 + 3y
2y – 4 = 4 + 3y
Y = -8
X = -10
The numbers are -10 and -8.