Answer:x = 11/8 and y = -1/4.
Explanation:
To solve the system of simultaneous equations:
2x + 3y = 2 --- Equation (1)
4x + 2y = 5 --- Equation (2)
We can use the elimination method, which involves multiplying one or both equations by a constant so that when we add or subtract them, one of the variables is eliminated.
Multiplying Equation (1) by 2, we get:
4x + 6y = 4 --- Equation (3)
Now we can subtract Equation (2) from Equation (3):
4x + 6y = 4
(4x + 2y = 5)
4y = -1
Dividing both sides by 4, we get:
y = -1/4
Substituting y = -1/4 into Equation (1), we get:
2x + 3(-1/4) = 2
Simplifying:
2x - 3/4 = 2
2x = 2 + 3/4
2x = 8/4 + 3/4
2x = 11/4
Dividing both sides by 2:
x = 11/8
Therefore, the solution to the system of simultaneous equations is:
x = 11/8 and y = -1/4.