The solution to the system of equations 2x + 3y = 10 and 3x - 4y = -2 is x = 2 and y = 2.
Given the system of equations in the question:
2x + 3y = 10
3x - 4y = -2
To determine the solution to the system of equations, we can use the elimination method:
2x + 3y = 10
3x - 4y = -2
Multiply the first equation by 4 and the second equation by 3:
We have:
8x + 12y = 40
9x - 12y = -6
Now, we add the two equations.
We have:
17x + 0 = 34
x = 34/17
x = 2
Now, plug x = 2 into the first equation and solve for y:
2x + 3y = 10
2(2) + 3y = 10
4 + 3y = 10
3y = 10 - 4
3y = 6
y = 6/3
y = 2
Therefore, the value of x is 2 and the value of y is 2.