solve by elimination method
3x+4y=4
6x+8y=8
3x+4y=4 ... (1)
6x+8y=8 ... (2)
If we multiply equation (1) by 2 and subtract from equation (2), we get
0 = 0
which means that the two equations represent coincident lines. This results in an infinite number of solutions:
Let y=t,
then
x=(4-4t)/3
y=t
for any value of t ∈R.
To solve the given system of equations using the elimination method, follow these steps:
Step 1: Multiply one or both equations by a constant so that the coefficients of either x or y are the same in both equations.
To make the coefficients of x the same, we can multiply the first equation by 2. This gives us:
Equation 1: 6x + 8y = 8
Step 2: Now, we can subtract Equation 1 from Equation 2 to eliminate the x variable.
Subtracting Equation 1 from Equation 2, we have:
(6x + 8y) - (6x + 8y) = 8 - 8
This simplifies to:
0 = 0
Step 3: We have obtained the equation 0 = 0, which means that the two equations are equivalent and represent the same line. Therefore, the original system of equations is dependent (infinite solutions) since the two lines overlap.
There are infinitely many solutions for this system of equations.