Solve the system of equations:
(1) 4х + 3y = 28
(2) 2x + 5y = 42
The solution is (x,y) = (1,8)
Explanation:
Subtract eq. 2 from eq. 1.
(4x + 3y) - (2x + 5y) = 28 - 42
--> 2x - 2y = -14
--> 2(x - y) = -14
--> x - y = -7
--> x = -7 + y
Substitute y for x to (1)
4(-7 + y) + 3y =28
--> -28 + 4y + 3y = 28
--> 7y = 28 - (-28)
--> 7y = 56
--> y = 8
It follows that
4x + 3y = 28
--> 4x + 3(8) = 28
--> 4x + 24 = 28
--> 4x = 4
--> x = 1
Hence, (x,y) = (1,8).
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