Rosie, this is the solution to the system of equations:
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2x - 3y = 6
2x - 6y = 9
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Step 1: Let's multiply by -1 the second equation, therefore we have:
2x - 3y = 6
-2x + 6y = -9
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Step 2: We eliminate x and solve for y, as follows:
-3y + 6y = 6 - 9
3y = -3
Dividing by 3 at both sides:
3y/3 = -3/3
y = -1
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Step 3: We substitute y and solve for x in the first equation, this way:
2x - 3 (-1) = 6
2x + 3 = 6
Subtracting 3 at both sides:
2x + 3 - 3 = 6 - 3
2x = 3
Dividing by 2 at both sides:
2x/2 = 3/2
x = 3/2
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Step 4: Now, let's prove x = 3/2 and y = -1 are right, replacing in the second equation, as follows:
2x - 6y = 9
2 (3/2) - 6 (-1) = 9
3 + 6 = 9
9 = 9
We proved that x = 3/2 and y = -1 are correct.