Answer:
x = 26/7
y = 10/7
Explanation:
To find the values of x and y that satisfy the system of equations:
1. 3x + 2y = 14
2. x = 4y - 2
You can solve this system using the substitution method. Start by solving equation (2) for x:
x = 4y - 2
Now, substitute this expression for x into equation (1):
3(4y - 2) + 2y = 14
Now, distribute the 3 on the left side:
12y - 6 + 2y = 14
Combine like terms:
14y - 6 = 14
Add 6 to both sides of the equation:
14y = 14 + 6
14y = 20
Now, divide by 14 to solve for y:
y = 20 / 14
y = 10 / 7
Now that you have found the value of y, you can substitute it back into equation (2) to find x:
x = 4(10 / 7) - 2
x = (40 / 7) - (14 / 7)
x = (40 - 14) / 7
x = 26 / 7
So, the values that satisfy the system of equations are:
x = 26/7
y = 10/7