Problem 1 :
x + 2y = 20
2x + y = 19
Problem 2 :
3x - 2y = -2
4x - 3y = -4
Problem 3 :
9x + 4y = 11
3x - 10y = -2
Problem 4 :
4x + 3y = 21
5x + 2y = 21
Problem 5 :
-3x - 5y = -7
-4x - 3y = -2
Problem 6 :
8x + 4y = 12
7x + 3y = 10
Problem 7 :
4x + 3y = -7
-2x - 5y = 7
1. Answer
x + 2y = 20 ---> (1)
2x + y = 19 ---> (2)
Comparing coefficients of x and y,
Coefficients of x are 1 and 2 Coefficients of y are 2 and 1 |
Not same Not same |
Both x terms and y terms have different coefficients in the above system of equations.
Let's try to make the coefficients of y terms equal.
To make the coefficients of y terms equal, we have to find the least common multiple 2 and 1.
The least common multiple of 2 and 1 is 2.
Multiply the second equation by -2 in order to make the coefficient of y as -2.
(1) ---> x + 2y = 20
(2) ⋅ -2 ---> -4x - 2y = -38
Now, we can add the two equations and eliminate y as shown below.
x = 6
Substitute 6 for x in (1).
6 + 2y = 20
2y = 14
y = 7
So, the values of x and y are 6 and 7 respectively.
2. Answer
3x - 2y = -2 ---> (1)
4x - 3y = -4 ---> (2)
Coefficients of x are 3 and 4 Coefficients of y are -2 and -3 |
Not same Not same |
The least common multiple of 2 and 3 is 6.
Multiply the first equation by -3 in order to make the coefficient of y as 6 and multiply the second equation by 2 in order to make the coefficient of y as -6.
(1) ⋅ -3 ---> -9x + 6y = 6
(2) ⋅ 2 ---> 8x - 6y = -8
Now, we can add the two equations and eliminate y as shown below.
x = 2
Substitute 2 for x in (1).
3(2) - 2y = -2
6 - 2y = -2
-2y = -8
y = 4
So, the values of x and y are 2 and 4 respectively.
3. Answer
9x + 4y = 11 ---> (1)
3x - 10y = -2 ---> (2)
Both x terms and y terms have different coefficients in the above system of equations.
Let's try to make the coefficients of x terms equal.
To make the coefficients of x terms equal, we have to find the least common multiple 9 and 3.
The least common multiple of 9 and 3 is 9.
Multiply the second equation by -3 in order to make the coefficient of x as -9.
(1) ---> 9x + 4y = 11
(2) . -3 ---> -9x + 30y = 6
Now, we can add the two equations and eliminate x as shown below.
y = 17/34
y = 1/2
Substitute 1/2 for y in (1).
9x + 4(1/2) = 11
9x + 2 = 11
9x = 9
x = 1
So, the values of x and y are 1 and 1/2 respectively.
4. Answer
4x + 3y = 21 ---> (1)
5x + 2y = 21 ---> (2)
Both x terms and y terms have different coefficients in the above system of equations.
Let's try to make the coefficients of x terms equal.
To make the coefficients of y terms equal, we have to find the least common multiple 3 and 2.
The least common multiple of 3 and 2 is 6.
Multiply the first equation by 2 in order to make the coefficient of y as 6 and multiply the second equation by -3 in order to make the coefficient of y as -6.
(1) . 2 ---> 8x + 6y = 42
(2) . -3 ---> -15x - 6y = -63
Now, we can add the two equations and eliminate y as shown below.
x = 21/7
x = 3
Substitute 3 for x in (1).
4(3) + 3y = 21
12 + 3y = 21
3y = 9
y = 3
So, the values of x and y are 3 and 3 respectively.
5. Answer
-3x - 5y = -7 ---> (1)
-4x - 3y = -2 ---> (2)
Both x terms and y terms have different coefficients in the above system of equations.
Let's try to make the coefficients of y terms equal.
To make the coefficients of y terms equal, we have to find the least common multiple 4 and 3.
The least common multiple of 4 and 3 is 12.
Multiply the first equation by 3 in order to make the coefficient of y as 12 and multiply the second equation by -4 in order to make the coefficient of y as -12.
(1) . 3 ---> 24x + 12y = 36
(2) . -4 ---> -28x - 12y = -40
Now, we can add the two equations and eliminate y as shown below.
x = 1
Substitute 1 for x in (1).
8(1) + 4y = 12
8 + 4y = 12
4y = 4
y = 1
So, the values of x and y are 1 and 1 respectively.
6. Answer
4x + 3y = -7 ---> (1)
-2x - 5y = 7 ---> (2)
Both x terms and y terms have different coefficients in the above system of equations.
Let's try to make the coefficients of x terms equal.
To make the coefficients of x terms equal, we have to find the least common multiple 4 and 2.
The least common multiple of 4 and 2 is 4.
Multiply the second equation by 2 in order to make the coefficient of x as 4.
(1) ---> 4x + 3y = -7
(2) . 2 ---> -4x - 10y = 14
y = -1
Substitute -1 for y in (1).
4x + 3(-1) = -7
4x - 3 = -7
4x = -4
x = -1
So, the values of x and y are -1 and -1 respectively.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM