Solve by the elimination method.
2x – 3y = 2
3x + 2y = 29

x=7, y=4

Step-by-step explanation:

2x – 3y = 2 , this will be equation 1.

3x + 2y = 29, this will be equation 2.

We have to make a letter have the same coefficient in the two equations.

lets make x have the same coefficient in the two equations.

Multiply the whole of equation 1 by 3.

3(2x - 3y = 2)

6x - 9y = 6, this will be equation 3.

Multiply the whole of equation 2 by 2.

2(3x + 2y = 29)

6x + 4y = 58, this will be equation 4.

Now let's begin.

We'll put equation 4 up so it will be easier to solve.

6x + 4y = 58, equation 4.

6x - 9y = 6, equation 3.

Let's get rid of 6x, so we can find the value of y; we'll have to subtract equation 3 fron equation 4. Please take note of the signs, (+) and (-).

(6x-6x) + (4y-(-9y)) = (58-6)

Notice the sign change.

0 + (4y + 9y) = 52

13y = 52

Divide both sides by 13.

13y/13 = 52/13

y = 4

To find x, we'll have to substitute y into equation 1 or equation 2. Let's use both.

EQUATION 1

2x – 3y = 2

2x - 3(4) = 2

2x - 12 = 2

Add 12 to both sides.

2x - 12 (+12) = 2 (+12)

2x - 0 = 14

2x = 14

Divide both sides by 2.

2x/2 = 14/2

x = 7

EQUATION 2

3x + 2y = 29

3x + 2(4) = 29

3x + 8 = 29

Subtract 8 from both sides.

3x + 8 (-8) = 29 (-8)

3x + 0 = 21

3x = 21

Divide both sides by 3.

3x/3 = 21/3

x = 7

Therefore, the answers are x=7, and y=4.

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