Question

Solve each equation for x and y:

2x + 3y = 10
4x - 2y = 5
a) x = 2, y = 2
b) x = 3, y = 1
c) x = 1, y = 3
d) x = 2, y = 3

Answer 1

Using elimination method, the system of equations 2x + 3y = 10 and 4x - 2y = 5 is solved to find that x = 5/4 and y = 15/8. None of the provided options match this solution.

Step-by-step explanation:

To solve the given pair of equations 2x + 3y = 10 and 4x - 2y = 5 for x and y, we can use the method of substitution or elimination. For the purpose of this explanation, let's use the elimination method.

1. Multiply the first equation by 2, to make the coefficient of y in both equations the same with opposite signs. This gives us 4x + 6y = 20.
2. Now, subtract the second given equation from the new equation we just formed. This will eliminate y and give us 4x + 6y - (4x - 2y) = 20 - 5, which simplifies to 8y = 15. Thus, y = 15/8.
3. Substitute the value of y back into the first given equation to find x. This will give us 2x + 3(15/8) = 10, which simplifies to x = 5/4.

The solution to the system of equations is x = 5/4 and y = 15/8. None of the options provided (a, b, c, d) are correct.