Solve the system by elimination.
3x−3y=1
x−y=15
To solve the system by elimination, we can multiply the second equation by 3 to make the coefficients of x in both equations the same.
Original system:
3x − 3y = 1
x − y = 15
Multiply the second equation by 3:
3(x − y) = 3(15)
3x − 3y = 45
Now the system becomes:
3x − 3y = 1
3x − 3y = 45
Subtract the first equation from the second equation:
(3x − 3y) − (3x − 3y) = 45 − 1
0 = 44
This equation is contradictory and cannot be true. Therefore, the system is inconsistent and has no solution.
To solve the system of equations by elimination, we need to eliminate one variable by manipulating the equations so that the coefficients of one of the variables are the same.
First, let's multiply the second equation by 3 to make the coefficient of x the same as the first equation.
3(x - y) = 3(15)
3x - 3y = 45
Now, we have the system of equations:
3x - 3y = 1 (equation 1)
3x - 3y = 45 (equation 2)
Now, we can subtract equation 1 from equation 2 to eliminate the variable y:
(3x - 3y) - (3x - 3y) = 45 - 1
0 = 44
The equation 0 = 44 is not possible, which means the system of equations is inconsistent. There is no solution for this system.
To solve the system of equations by elimination, we need to eliminate one variable by adding or subtracting the two equations. Let's solve the system of equations step by step:
First, let's rewrite the equations:
1) 3x - 3y = 1
2) x - y = 15
To eliminate one of the variables, we need to make the coefficients of either x or y the same. In this case, it's easier to eliminate the y variable.
To eliminate the y variable, we can multiply the second equation by 3 and add the equations together. This will give us a new equation without the y variable.
Multiply equation (2) by 3:
3*(x - y) = 3*15
3x - 3y = 45
Now, we have the following equations:
1) 3x - 3y = 1
3) 3x - 3y = 45
Next, subtract equation (1) from equation (3) to eliminate the y variable:
(3x - 3y) - (3x - 3y) = 45 - 1
0 = 44
However, this equation simplifies to 0 = 44, which is not true. This means that the original system of equations is inconsistent, and has no solution. In other words, there is no pair of values for x and y that satisfies both equations simultaneously.
Therefore, the system of equations is inconsistent and has no solution.