Question

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

Answer 1

Answer:

${x,y}={3,3}$

Step-by-step 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}

Answer 2

Answer:

$(3,3)$

Step-by-step explanation:

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

$\mathrm{Substitute\:}x=\frac{15-3y}{2}$

$\begin{bmatrix}\frac{15-3y}{2}+y=6\end{bmatrix}$

$\begin{bmatrix}\frac{15-y}{2}=6\end{bmatrix}$

$y=3$

$\mathrm{For\:}x=\frac{15-3y}{2}$

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

$x=\frac{15-3\cdot \:3}{2}$

$15-9=6$

$\frac{6}{2}=3$

$x=3$