x-y=2
2x+3y=14
To solve the system of equations, we can use the method of substitution or elimination.
Method 1: Substitution
1. Solve the first equation for x in terms of y:
x = y + 2
2. Substitute the value of x in the second equation:
2(y + 2) + 3y = 14
2y + 4 + 3y = 14
5y + 4 = 14
5y = 10
y = 2
3. Substitute the value of y back into the first equation to find x:
x - 2 = 2
x = 4
Therefore, the solution to the system of equations is x = 4 and y = 2.
Method 2: Elimination
1. Multiply the first equation by 3 and the second equation by 2 to make the coefficient of y the same in both equations:
3(x - y) = 3(2)
2(2x + 3y) = 2(14)
3x - 3y = 6
4x + 6y = 28
2. Add the two equations together to eliminate the y term:
(3x - 3y) + (4x + 6y) = 6 + 28
7x + 3y = 34
3. Solve this equation for x:
7x = 34 - 3y
x = (34 - 3y)/7
4. Substitute the value of x into the first equation to solve for y:
(34 - 3y)/7 - y = 2
34 - 3y - 7y = 14
34 - 10y = 14
10y = 20
y = 2
5. Substitute the value of y back into the first equation to find x:
x - 2 = 2
x = 4
The solution to the system of equations is the same as in method 1: x = 4 and y = 2.