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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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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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