Question

Find the value of x+y, If 15x + 17y= 21 and 17x+15y= 11​

Answer 1

$\begin{gathered}\begin{gathered}\bf \:Given-\begin{cases} &\sf{15x + 17y = 21} \\ &\sf{17x + 15y = 11} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf \: To \: Find - \begin{cases} &\sf{value \: of \: x + y}\end{cases}\end{gathered}\end{gathered}$

$\large\underline{\sf{Solution-}}$

↝ Given equations are

$\: \: \: \: \: \: \: \: \bull \sf \: 15x + 17y = 21 - - - (1)$

$\: \: \: \: \: \: \: \: \bull \sf \: 17x + 15y = 11 - - - (2)$

↝ On adding equation (1) and equation (2), we get

$\rm :\longmapsto\:15x + 17y + 17x + 15y = 21 + 11$

$\rm :\longmapsto\:(15x + 17x) + (17y + 15y) = 32$

$\rm :\longmapsto\:32x + 32y = 32$

$\rm :\longmapsto\:32(x + y) = 32$

$\bf\implies \:x + y = 1$

$\overbrace{ \underline { \boxed { \bf \therefore \: The \: value \: of \: x + y \: is \:1}}}$

Additional Information :-

There are 4 methods to solve this type of pair of linear equations.

• 1. Method of Substitution

• 2. Method of Eliminations

• 3. Method of Cross Multiplication

• 4. Graphical Method

To solve systems using substitution, follow this procedure:

• Select one equation and solve it to get one variable in terms of second variables.

• In the second equation, substitute the value of variable evaluated in Step 1 to reduce the equation to one variable.

• Solve the new equation to get the value of one variable.

• Substitute the value found in to any one of two equations involving both variables and solve for the other variable.

The Elimination Method

• Step 1: Multiply each equation by a suitable number so that the two equations have the same leading coefficient.

• Step 2: Subtract the second equation from the first to eliminate one variable.

• Step 3: Solve this new equation for variable.

• Step 4: Substitute this value of variable into either Equation 1 or Equation 2 above and solve for other variable.

Answer 2

Step-by-step explanation:

15x+17y = 21

17x+15y = 11

15x+17y+17x+15y = 21+11

32x+32y = 32

32(x+y) = 32

x+y = 32/32

x+y = 1