Final answer:
We can eliminate the variable x by manipulating the equations so that the coefficients of x are the same but with opposite signs. The solution to the system of equations is x = 3 and y = -4.
Step-by-step explanation:
To solve this system of equations, we can use the method of elimination by addition or subtraction. To solve this system of equations, we can use the method of elimination by addition or subtraction. To eliminate a variable, we want to manipulate the equations so that the coefficients of the variable are the same but with opposite signs.
In this case, let's focus on eliminating the variable x. If we multiply the first equation by 2 and the second equation by 3, we will have the same coefficient for x with opposite signs.
2(-3x + 4y) = 2(-25) → -6x + 8y = -50
3(2x - 5y) = 3(26) → 6x - 15y = 78
Now, if we add these two equations, the x term will cancel out: (-6x + 8y) + (6x - 15y) = -50 + 78 → -7y = 28
To solve for y, divide both sides of the equation by -7: -7y/-7 = 28/-7 → y = -4
Now, substitute the value of y=-4 into one of the original equations to solve for x. Let's use the first equation: -3x + 4(-4) = -25 → -3x - 16 = -25 → -3x = -9 → x = 3
Therefore, the solution to the system of equations is x = 3 and y = -4.