Final answer:
To solve the system of equations by elimination, multiply one of the equations by a suitable number so that the coefficients of one of the variables are the same. Then, subtract the equations to eliminate one variable. Finally, solve for the remaining variables.
Step-by-step explanation:
To solve the system of equations 4x + 3y = 25 and 3x = x + 2y - 1 by elimination, we need to eliminate one variable by manipulating the equations. We can start by multiplying the second equation by 3 to make the coefficients of y the same. This gives us 9x = 3x + 6y - 3. Now, we can subtract the second equation from the first equation, which eliminates the x variable. This gives us 4x - 9x + 3y - 6y = 25 - (-3), which simplifies to -5x - 3y = 28. Now, we can solve this new equation for one variable and substitute the value back into one of the original equations to find the other variable.
We can multiply the new equation by -4 to make the coefficient of x positive and equal to 20. This gives us 20x + 12y = -112. Now, we can substitute 3x = x + 2y - 1 into this equation to eliminate the x variable. This gives us 20(x + 2y - 1) + 12y = -112, which simplifies to 32y - 20 = -112. Solving this equation for y, we get y = -3. Substituting this value back into 3x = x + 2y - 1, we can solve for x to get x = 6.