Solve by elimination method
3x+4y=5
6x+8y=10
It doesn't solve. Multiply the first equation by 2 and that gives you the second one.
To solve the system of equations using the elimination method, we'll apply the following steps:
1. Multiply one or both equations by constants, if necessary, so that the coefficients of either x or y in one equation are opposites of those in the other equation. In this case, both equations have the same coefficients, so we don't need to multiply either equation by any constant.
2. Add or subtract the two equations to eliminate one variable. The goal is to create a new equation with only one variable in it. Let's eliminate x in this case. We can achieve this by multiplying the first equation by -2 and the second equation by 1:
(-2) * (3x + 4y) = (-2) * (5)
(1) * (6x + 8y) = (1) * (10)
Simplifying these equations gives us:
-6x - 8y = -10
6x + 8y = 10
Adding these two equations eliminates x:
(-6x + 6x) + (-8y + 8y) = -10 + 10
0 + 0 = 0
We are left with the equation 0 = 0, which means this equation is true for any value of x and y.
3. Determine the values of x and y. Since the last equation is always true, there are infinitely many solutions to this system of equations. Any values of x and y that satisfy the original equations will solve the system. In this case, the solution is represented by the equation 0 = 0.
So, the system of equations is dependent and consistent with an infinite number of solutions.