Question

2x + 3y = 15
x + y = 6
what is x and what is y

Answer 1

`(3,3)`

Explanation:

`\begin{bmatrix}2x+3y=15\\ x+y=6\end{bmatrix}`

`\mathrm{Substitute\:}x=(15-3y)/(2)`

`\begin{bmatrix}(15-3y)/(2)+y=6\end{bmatrix}`

`\begin{bmatrix}(15-y)/(2)=6\end{bmatrix}`

`y=3`

`\mathrm{For\:}x=(15-3y)/(2)`

`\mathrm{Substitute\:}y=3`

`x=(15-3\cdot \:3)/(2)`

`15-9=6`

`(6)/(2)=3`

`x=3`

Answer 2

`{x,y}={3,3}`

Explanation:

System of Linear Equations entered :

`[1] 2x + 3y = 15\\ [2] x + y = 6`

Graphic Representation of the Equations :

3y + 2x = 15 y + x = 6

Solve by Substitution :

// Solve equation [2] for the variable y

[2] y = -x + 6

// Plug this in for variable y in equation [1]

[1] 2x + 3•(-x +6) = 15

[1] -x = -3

// Solve equation [1] for the variable x

[1] x = 3

// By now we know this much :

x = 3

y = -x+6

// Use the x value to solve for y

y = -(3)+6 = 3

Solution :

{x,y} = {3,3}