Final answer:
Solving the system of equations using the elimination method involves manipulating the equations to eliminate one variable and then solving for the other. Plug the found value into one of the original equations to find the remaining variable.
Step-by-step explanation:
To solve the system of equations: 7y + 10x = -11, and 4y - 3x = -15, you can use either the substitution method, the elimination method, or a matrix method. For this example, we'll use the elimination method to find the values of y and x.
First, let's multiply the second equation by 2.5 to eliminate the y terms. So, the second equation (multiplied by 2.5) becomes: 10y - 7.5x = -37.5.
Now, we add this new second equation to the first equation:
7y + 10y + 10x - 7.5x = -11 - 37.5
This simplifies to:
17y + 2.5x = -48.5.
We can now solve for y by substituting the second original equation into this result. From the second equation: x = (4y + 15) / 3. Now substitute for x:
17y + 2.5((4y + 15)/3) = -48.5.
Solve for y to get the value of y.
Once y is found, substitute back into one of the original equations to find the value for x.