Answer:
4. (x, y) = (3, 4)
5. (x, y) = (8, 13)
6. (x, y) = (2, 12)
Explanation:
4. Substitute the expression for y given by the second equation into the first equation:
-3x +4(3x -5) = 7
-3x +12x -20 = 7 . . . . eliminate parentheses
9x = 27 . . . . . . . . . . . add 20, collect terms
x = 3 . . . . . . . . . . . . . . divide by 9
y = 3·3 -5 = 4 . . . . . . . substitute for x in the second equation
The solution is (x, y) = (3, 4).
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Check
-3·3 +4·4 = 7 . . . . true
4 = 3·3 -5 . . . . . . true (we used this to find y, so we don't really need to check this)
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5. Rearrange the first equation to make an expression for y, then use that in the second equation.
y = 2x -3
-6x +4(2x -3) = 4 . . . . substitute for y
-6x +8x -12 = 4 . . . . . . eliminate parentheses
2x = 16 . . . . . . . . . . . . add 12, collect terms
x = 8 . . . . . . . . . . . . . . divide by 2
y = 2·8 -3 = 13
The solution is (x, y) = (8, 13).
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Check
-2·8 + 13 = -3 . . . . true (we used this to find y, so no real need to check)
-6·8 +4·13 = 4 . . . . true
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6. Divide the first equation by 2 and add 5x to make an expression for y.
y = 5x +2
-9x +3(5x +2) = 18 . . . . . substitute for y in the second equation
-9x +15x +6 = 18 . . . . . . eliminate parentheses
6x = 12 . . . . . . . . . . . . . . subtract 6, collect terms
x = 2 . . . . . . . . . . . . . . . . divide by 6
y = 5·2 +2 = 12 . . . . . . . find y using the expression we have for it
The solution is (x, y) = (2, 12).
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Check
-10·2 +2·12 = 4 . . . . true
-9·2 +3·12 = 18 . . . . true