Solve using the elimination method. Show all work. If the system has no solution or an infinite number of solutions, state this.
3x+7y=77
-2x+7y=42
Subtract the second equation from the first.
5x = 35
You do the rest
2x+6y=4
3x-7y=6
To solve this system of equations using the elimination method, we will aim to eliminate one variable by adding or subtracting the equations. Let's start by multiplying the second equation by 3 to make the x-coefficients the same in both equations:
Original Equations:
1) 3x + 7y = 77
2) -2x + 7y = 42
Multiply Equation 2 by 3:
3) (3 * -2x) + (3 * 7y) = (3 * 42)
-6x + 21y = 126
Next, we'll subtract Equation 1 from Equation 3 to eliminate the x variable:
(Equation 3) - (Equation 1)
(-6x + 21y) - (3x + 7y) = 126 - 77
-6x + 21y - 3x - 7y = 49
-9x + 14y = 49
Now we have a new equation:
4) -9x + 14y = 49
We can see that Equation 4 is different from Equation 1, so these two equations are not the same. Thus, this system has no solutions.