7.3 Answers with explanation
2. Since the x terms are equal, we would need to subtract equation 2 from equation 1. Then we would have a
resulting equation that we would need to solve for y and get a value for that y. Then we would substitute that value
into either of the equations to get the value for x.
7.
-9x + 4y = -17
9x – 6y = 3
-2y=-14
y=7
Add both equations because the coefficients for x are equal and opposites
Substitute the 7 into y in either equation!
-9x + 4(7) = -17
-9x +28=-17
-9x =-45
x=5
The solution is (5,7).
11.
2x – y = 7
2x + 7y=31
-8y=-24
y=3
Subtract the two equations because the coefficients of x are equal
Substitute the 3 into y in either equation!
2x + 7(3) = 31
2x +21 = 31
2x= 10
x=5
The solution is (5,3).
13.
5x + 6y = 50
-x + 6y = 26
Subtract the equations because the coefficients of y are equal
6x =24
x=4
Substitute that 4 into x in either equation!
-4 + 6y = 26
6y = 30
y =5
The solution is (4,5).
17.
-8y + 6x = 36
6x – y = 15
We need to adjust EQN #1 because we need the x term first and the y term second.
So the first EQN should be written like 6x – 8y = 36
6x - 8y = 36
6x – y = 15
Subtract the two EQNs b/c the x terms are equal
-7y = 21
Divide by -7 on both sides
y=-3
6x – (-3) =15
Substitute -3 in ( ) for y in the second EQN
6x + 3 = 15
Subtract 3 on both sides
6x =12
Divide by 6 on both sides
x=2
The solution is (2, -3).
7.3 Answers with explanation
21.
-5x + y = -23
-y = 3x – 9
-3x -3x
-5x + y = -23
-3x – y = -9
-8x = -32
x=4
-y = 3(4) -9
-y = 12-9
-y=3
y = -3
The solution is (4,-3).
We need to adjust EQN # 2 to put it into standard form like EQN #1
Subtract 3x on both sides to get it into standard form
Add the two EQNs b/c the y term coefficients are opposites
Divide by -8 on both sides
Substitute the 4 in for x in the second original EQN
Divide by -1 on both sides
23. The two EQNs should be subtracted rather than added. x= 4/3 y =-4/3
24. They should’ve added the 3x over so instead of -3x it should be positive 3x. y = 9 and x = 5
35. The perimeter EQN is ALWAYS 2W + 2L =P (for perimeter) since the perimeter is 14 the EQN would be
2W + 2L = 14
The other EQN will come from the sentence of twice its length is equal to one less than 4 times its width
2L
=
4W -1
So our system is 2W + 2L = 14
2L = 4w – 1
The length is 4.5 ft and the width is 2.5ft.
39. The set up is on the page. Basically we are trying to find the speed in still water and the speed of the current
(those get the variables) so…
x – y =4.3
x + y = 4.9
The boat would be going slower if it was fighting the current.
The boat would go faster if the current was added to its speed.
The speed of the current is 0.3 m/sec and the speed of the boat in still water is 4.6 m/sec.
40.
x + 5y =22.45
x + 7y = 25.45
The fee is $14.95 and the cost per quart of oil is $1.50.