Answer:
x=7, y=4
Step-by-step explanation:
2x – 3y = 2
, this will be equation 1.
3x + 2y = 29, this will be equation 2.
<em><u>We have to make a letter have the same coefficient in the two equations.</u></em>
lets make x have the same coefficient in the two equations.
<u><em>Multiply the whole of equation 1 by 3.</em></u>
3(2x - 3y = 2)
6x - 9y = 6, this will be equation 3.
<u><em>Multiply the whole of equation 2 by 2.</em></u>
2(3x + 2y = 29)
6x + 4y = 58, this will be equation 4.
<em><u>Now let's begin.</u></em>
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
<u><em>To find x, we'll have to substitute </em></u><u><em>y</em></u><u><em> into equation 1 or equation 2. Let's use both.</em></u>
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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