1. Solve the systems of equations by elimination
3x-5y = 29
2x+3y = -6
2. Solve the systems of equations by elimination
2x+5y = -20
7x + 5y = 5
3. Solve the systems of equations by elimination
3x-5y = 29
2x + 3y = -6
4. Solve the systems of equations by elimination
2x+4y = -8
3x-5y =21
5. A system of equations is given below:
X +2y = 5
2x+y = 4
Which system of equations does not have the same solution?
A. 3x + 6y = 15
2x + y = 4
B. X + 2y = 5
6x + 3y = 12
C. 4x + 8y = 20
2x + y = 4
D. x + 2y = 5
4x + 2y = 12
1. To solve the system of equations by elimination:
Multiply the first equation by 2 and the second equation by 3 to make the coefficients of x in both equations the same:
6x - 10y = 58
6x + 9y = -18
Now subtract the second equation from the first equation:
(6x - 10y) - (6x + 9y) = 58 - (-18)
-19y = 76
Divide both sides by -19:
y = -4
Substitute the value of y back into one of the original equations, such as the first equation:
3x - 5(-4) = 29
3x + 20 = 29
Subtract 20 from both sides:
3x = 9
Divide both sides by 3:
x = 3
The solution to the system of equations is x = 3 and y = -4.
2. To solve the system of equations by elimination:
Multiply the first equation by -7 to make the coefficients of x in both equations the same:
-14x - 35y = 140
7x + 5y = 5
Now add the two equations:
-14x - 35y + 7x + 5y = 140 + 5
-7x - 30y = 145
Divide both sides by -5:
x + 6y = -29
The system of equations is inconsistent since there is no unique solution.
3. To solve the system of equations by elimination:
Multiply the second equation by -3 to make the coefficients of x in both equations the same:
3x - 5y = 29
-6x - 9y = 18
Now add the two equations:
3x - 5y + (-6x) + (-9y) = 29 + 18
-3x - 14y = 47
Divide both sides by -14:
x + (3/14)y = -47/14
The system of equations is inconsistent since there is no unique solution.
4. To solve the system of equations by elimination:
Multiply the first equation by 2 and the second equation by 4 to make the coefficients of x in both equations the same:
4x + 8y = -16
12x - 20y = 84
Now subtract the first equation from the second equation:
(12x - 20y) - (4x + 8y) = 84 - (-16)
8x - 28y = 100
Divide both sides by 4:
2x - 7y = 25
The system of equations is inconsistent since there is no unique solution.
5. The system of equations B does not have the same solution.