Heya!
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Lets solve for the system given in the question.
4x − 5y = 2
3x − y = 8
Rewrite both equations.
Solve 3x − y = 8 for y.
3x - y = 8
~Subtract 3x to both sides
3x - y - 3x = 8 - 3x
~Simplify
-y = -3x + 8
~Divide -1 to both sides
-y/-1 = -3x+8/-1
~Simplify
y = 3x - 8
Substitute 3x - 8 for y in 4x − 5y = 2
4x - 5(3x - 8) = 2
~Simplify
-11x + 40 = 2
~Subtract 40 to both sides
-11x + 40 - 40 = 2 - 40
~Simplify
-11x = -38
~Divide -11 to both sides
-11x/-11 = -38/-11
~Simplify
x = 38/11
Substitute 38/11 for x in y = 3x - 8
y = 3(38/11) - 8
~Simplify
y = 26/11
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The solution to the system is (38/11, 26/11).
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The answer is A. 4x − 5y = 2, 10x − 7y = 18
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Lets solve for the system given in the answer.
4x − 5y = 2
10x − 7y = 18
Rewrite both equations.
Solve 4x − 5y = 2 for x.
4x − 5y = 2
~Add 5y to both sides
4x - 5y + 5y = 2 + 5y
~Simplify
4x = 2 + 5y
~Divide 4 to both sides
4x/4 = 2+5y/4
~Simplify
x = 1/2 + 4/5y
Substitute 1/2 + 4/5y for x in 10x − 7y = 18
10(1/2 + 4/5y) − 7y = 18
~Simplify
11/2y + 5 = 18
~Subtract 5 to both sides
11/2y + 5 - 5 = 18 - 5
~Simplify
11/2y = 13
~Divide both sides by 11/2
11/2y ÷ 11/2 = 13 ÷ 11/2
~Simplify
y = 26/11
Substitute 26/11 for in x = 1/2 + 4/5y
x = 1/2 + 4/5(26/11)
~Simplify
38/11
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The solution to the system is (38/11, 26/11).
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That makes it the correct answer.
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Best of Luck!
