Same y terms but both signs are positive

Introduction to Same y Terms with Both Signs Positive

When dealing with a system of equations where the ‘y’ terms are identical and both signs are positive, we can use various algebraic methods to solve for both x and y.

Steps for Solving Equations with Same y terms and Positive Signs

Given two equations in the form of ax + by = c and dx + ey = f, where by and ey have positive signs.
If the coefficients of ‘y’ in both equations are the same, we can subtract one equation from the other.
Subtracting the equations will eliminate ‘y’ since they have the same coefficients and both signs are positive.
You are then left with an equation with just one variable, ‘x’, which can be solved with straightforward algebraic methods.
Once the value of ‘x’ is determined, we can substitute this back into one of the original equations to find the value of ‘y’.

Example Case

Let’s consider the system of equations: 2x + 3y = 12 and 5x + 3y = 23.
Both have the same ‘y’ term, and both ‘y’ term coefficients are positive. If we subtract the first equation from the second, we would be left with: 3x = 11.
The value of ‘x’ can be straightforwardly found by dividing both sides by 3, giving us: x = 11/3.
This value would then be substituted into one of the initial equations to find ‘y’. For example, substituting x = 11/3 into the first original equation gives 2(11/3) + 3y = 12, which simplifies to: y = 2.

Final Notes

When dealing with equations with same ‘y’ terms and both signs positive, the subtractive method usually works best.
Accuracy in mathematical operations including addition, subtraction, and division is especially critical.
Always ensure to substitute the found value back into one of the original equations to work out the remaining variable. This not only helps find the answer but also serves as a check to verify the correctness of the derived solution.