Solve for x and y: 7(y + 3) - 2(x + 2) = 14, 4(y - 2) + 3(x - 3) = 2

Solution:

Step 1: Simplify the linear equations.

7(y + 3) - 2(x + 2) = 14 --- eq(1)

4(y - 2) + 3(x - 3) = 2 --- eq(2)

Rewrite them as:

⇒ 7y + 21 - 2x - 4 = 14 or 7y - 2x = -3 --- eq(3)

⇒ 4y - 8 + 3x - 9 = 2 or 4y + 3x = 19 --- eq(4)

Let us use the elimination method to solve the equations.

Step 2: Multiply equation (3) by 3 and equation (4) by 2.

21y - 6x = - 9 --- eq(5)

8y + 6x = 38 --- eq(6)

Step 3: Add equation (5) and (6).

29y = 29

y = 1

Step 4: Substitute the value of y in equation 3.

7 (1) - 2x = -3

2x = 10

x = 5

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Solve for x and y: 7(y + 3) - 2(x + 2) = 14, 4(y - 2) + 3(x - 3) = 2

Summary:

The values of x and y for the equations 7(y + 3) - 2(x + 2) = 14, 4(y - 2) + 3(x - 3) = 2 are 5 and 1 respectively.