How can I use substitution in the problem 2x-y=5, 3x-2y=9 ? How can I use substitution in the problem 2x-y=5, 3x-2y=9 ?
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To solve
2x - y = 5 ...(1)
3x - 2y = 9 ...(2)
using substitution take (1)
2x - y = 5
=> y = 2x - 5
substitute in (2)
3x - 2(2x - 5) = 9
=> 3x - 4x + 10 = 9
=> -x = -1
=> x = 1
y = 2x - 5 = 2 - 5 = -3
The solution of the equations is x = 1 and y = -3
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We'll write the first equatino, isolating y to the left side. For this reason, we'll subtract 5 both sides:
2x - y - 5 = 0
We'll add y both sides:
y = 2x - 5 (1)
Now, we can replace y by it's expression into the 2nd equation:
3x - 2(2x - 5) = 9 <=> 3x - 4x + 10 = 9
We'll combine like terms:
-x + 10 = 9
We'll subtract 10 both sides:
-x = -1 <=> x = 1
We'll determine y:
y = 2x - 5
y = 2 - 5
y = -3
The solution of the system is represented by the pair: (1 ; -3).
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