3x+4y=5
6x+8y=10
solve using the elimination method but I do not know where to begin
Have you noticed that if you multiply the first equation by 2, you get the second equation?
If that happens there will be an infinite number of solutions, since you are really just given one equation.
e.g. if x = 1, y = 1/2 it works in both
if x = -1, y = 2, it works in both etc.
I am still very confused on how to find the ordered pairs and I guess I do not understand what you are saying.
To find the solution to the system of equations:
3x + 4y = 5 ...(Equation 1)
6x + 8y = 10 ...(Equation 2)
We can use either the substitution method or the elimination method. Let's solve it using the elimination method:
Step 1: Multiply Equation 1 by 2 to make the coefficients of x in both equations equal.
2(3x + 4y) = 2(5)
6x + 8y = 10 ...(Equation 1, after multiplying)
Now, the system of equations becomes:
6x + 8y = 10 ...(Equation 1)
6x + 8y = 10 ...(Equation 2)
Step 2: Subtract Equation 2 from Equation 1 to eliminate the x term.
(6x + 8y) - (6x + 8y) = (10 - 10)
0 = 0
The result of subtracting the two equations is 0 = 0, which means the two equations are equivalent. In other words, the equations represent the same line and have infinitely many solutions. The system is therefore dependent.
The equations given are not sufficient to determine unique values for variables x and y.