Solve the following systems of equations by substitution method.
1) y = -2 and 4x - 3y = 18
2) y = 6x - 11 and 2x + 3y = 7
3) x = -3y - 5 and 4x - 5y = -3
4) x = 5y - 7 and -2x - 3y = -12
5) 5x - 3y - 8 = 0 and 2x - 3y - 6 = 0
6) x - 3y - 11 = 0 and 5x + y - 7 = 0
7) 2x - 3y = -1 and y = x - 1
8) -4x + y = 6 and -5x - y = 21
9) In my pocket i have only 5 cent and 10 cent coins. How many of each type of coin do i have 24 coins altogether and their total value is $1.55 ?
1. Answer :
y = -2
4x - 3y = 18 ----(1)
Substitute y = -2 in (1).
4x - 3(-2) = 18
4x + 6 = 18
Subtract 6 from both sides.
4x = 12
Divide both sides by 4.
x = 3
So,
x = 3 and y = -2
2. Answer :
y = 6x - 11 ----(1)
2x + 3y = 7 ----(2)
Substitute y = 6x - 11 in (2).
2x + 3(6x - 11) = 7
2x + 18x - 33 = 7
20x - 33 = 7
Add 33 to both sides.
20x = 40
Divide both sides by 20.
x = 2
Substitute x = 2 in (1).
y = 6(2) - 11
= 12 - 11
= 1
So,
x = 2 and y = 1
3. Answer :
x = -3y - 5 ----(1)
4x - 5y = -3 ----(2)
Substitute x = -3y + 5 in (2).
4(-3y - 5) - 5y = -3
-12y - 20 - 5y = -3
-17y - 20 = -3
Add 20 to both sides.
17y = -17
Divide both sides by 17.
y = -1
Substitute y = -1 in (1).
x = -3(-1) - 5
= 3 - 5
= -2
So,
x = -2 and y = -1
4. Answer :
x = 5y - 7 ----(1)
-2x - 3y = -12 ----(2)
Substitute x = 5y - 7 in (2).
-2(5y - 7) - 3y = -12
-10y + 14 - 3y = -12
-13y + 14 = -12
Subtract 14 from both sides.
-13y = -26
Divide both sides by -13.
y = 2
Substitute y = 2 in (1).
x = 5(2) - 7
= 10 - 7
= 3
So,
x = 3 and y = 2
5. Answer :
5x + 3y - 8 = 0 ----(1)
2x - 3y - 6 = 0 ----(2)
Solve for 3y in (1).
5x + 3y - 8 = 0
Subtract 5x from both sides.
3y - 8 = -5x
Add 8 to both sides.
3y = -5x + 8
Substitute 3y = -5x + 8 in (2).
2x - (-5x + 8) - 6 = 0
2x + 5x - 8 - 6 = 0
7x - 14 = 0
Add 14 to both sides.
7x = 14
Divide both sides by 7.
x = 2
6. Answer :
x - 3y - 11 = 0 ----(1)
5x + y - 7 = 0 ----(2)
Solve for x in (1).
x - 3y - 11 = 0
Subtract 3y and 11 to both sides.
x = 3y + 11 ----(3)
Substitute x = 3y + 11 in (2).
5(3y + 11) + y - 7 = 0
15y + 55 + y - 7 = 0
16y + 48 = 0
Subtract 48 from both sides.
16y = -48
Divide both sides by 16.
y = -3
Substitute y = -3 in (3).
x = 3(-3) + 11
= -9 + 11
= 2
So,
x = 2 and y = -3
7. Answer :
2x - 3y = -1 ----(1)
y = x - 1 ----(2)
Substitute y = x - 1 in (1).
2x - 3(x - 1) = -1
2x - 3x + 3 = -1
-x + 3 = -1
Subtract 3 from both sides.
-x = -4
Multiply both sides by -1.
x = 4
Substitute x = x in (3).
y = 4 - 1
= 3
So,
x = 4 and y = 3
8. Answer :
-4x + y = 6 ----(1)
-5x - y = 21 ----(2)
Solve for y in (1).
-4x + y = 6
Add 4x to both sides.
y = 4x + 6 ----(3)
Substitute y = 4x + 6 in (2).
-5x - (4x + 6) = 21
-5x - 4x - 6 = 21
-9x - 6 = 21
Add 6 to both sides.
-9x = 27
Divide both sides by -9.
x = -3
Substitute x = -3 in (3).
y = 4(-3) + 6
= -12 + 6
= -6
So,
x = -3 and y = -6
9. Answer :
Let x be the number of 5 cent coins and y be the number of 10 cent coins.
Total number of coins = 24
x + y = 24 ------(1)
0.05x + 0.10xy = 1.55 ------(2)
From (1),
y = 24 - x
Applying the value of y in (2), we get
0.05x + 0.10(24 - x) = 1.55
0.05x + 2.4 - 0.10x = 1.55
-0.05x = 1.55 - 2.4
-0.05 x = -0.85
x = 0.85/0.05
x = 17
Applying the value of x in y = 24 - x
y = 24 - 17
y = 7
So, number of 5 cent coins is 17 and number of 10 cent coins is 7
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