Solve by substitution 3x - 4y = 9, 2x + y = 6

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kingattaskus12's profile pic

kingattaskus12 | (Level 3) Adjunct Educator

Posted on

Move all terms not containing `y` to the right-hand side of the equation.

`3x-4y=9`
`y=6-2x`


Since the equation was solved for `y` , replace all occurrences of `y` in the other equations with the solution `(6-2x)` .

`3x-4(6-2x)=9 `


Multiply `-4` by each term inside the parentheses.

`3x+8x-24=9`


Since `3x` and `8x` are like terms, add `8x` to `3x` to get `11x` .

`11x-24=9`


Move all terms not containing `x` to the right-hand side of the equation.

`11x=33 `


Since the equation was solved for `x` , replace all occurrences of `x ` in the other equations with the solution `(3)` .

`x=3`


Since the equation was solved for ` x` , replace all occurrences of ` x` in the other equations with the solution `(3).`

`y=6-2(3) `

Multiply `-2` by each term inside the parentheses.

`y=6-6`

Subtract 6 from 6 to get 0.

`y=0 `

This is the solution to the system of equations.

`x=3`


`y=0`

nikolao's profile pic

nikolao | High School Teacher | (Level 1) Adjunct Educator

Posted on

3x-4y=9-------------(1)

2x+y=6-------------(2)

multiply  (2) by 4

8x+4y=24----------(3)

Then add (1)+(3)

3x-4y+8x+4y=9+24

11x=33

x=33/11

x=3

Let's use x=3 in (2)

2(3)+y=6

6+y=6

y=6-6

y=0

So the answer is

x=3 and y=0

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The system of equations 3x - 4y = 9, 2x + y = 6 has to be solved by substitution.

3x - 4y = 9

=> 3x = 9 + 4y

=> `x = 3 + (4/3)*y`

Substitute for x in 2x + y = 6

=> `2*(3 + (4/3)*y) + y = 6`

=> `6 + 8/3*y + y = 6`

=> y = 0

x = 3

The solution of the given set of equations is x = 3 and y = 0

malkaam's profile pic

malkaam | Student, Undergraduate | (Level 1) Valedictorian

Posted on

3x - 4y = 9   ----(i)

2x + y = 6    ----(ii)

These simultaneous equations can be solved with the help of substitution method, consider eq(ii)

2x + y = 6

y = 6 - 2x

Input the value of y in eq(i)

3x - 4y = 9

3x - 4(6 - 2x) = 9

3x - 24 + 8x = 9 

3x -24 + 24 + 8x = 9 + 24           Add 24 to both sides

11x = 33

11x/11 = 33/11                           Divide 11 by both sides

x = 3

Now input this value in eq(ii)

2x + y = 6  

2(3) + y = 6

6 + y = 6

6 + y - 6 = 6 - 6

y = 0  

Now substitute both values in eq(i)

3x - 4y = 9

3(3) - 4(0) = 9

9 - 0 = 9

9 = 9

LHS = RHS

Proved.

x = 3

y = 0 Answer.

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