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

2 thoughts on “<br /> Find the value of x+y, If 15x + 17y= 21 and 17x+15y= 11​”

1. 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

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2. [tex]\begin{gathered}\begin{gathered}\bf \:Given-\begin{cases} &\sf{15x + 17y = 21} \\ &\sf{17x + 15y = 11} \end{cases}\end{gathered}\end{gathered}[/tex]

   [tex]\begin{gathered}\begin{gathered}\bf \: To \: Find – \begin{cases} &\sf{value \: of \: x + y}\end{cases}\end{gathered}\end{gathered}[/tex]

   [tex]\large\underline{\sf{Solution-}}[/tex]

   ↝ Given equations are

   [tex] \: \: \: \: \: \: \: \: \bull \sf \: 15x + 17y = 21 – – – (1)[/tex]

   [tex] \: \: \: \: \: \: \: \: \bull \sf \: 17x + 15y = 11 – – – (2)[/tex]

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

   [tex]\rm :\longmapsto\:15x + 17y + 17x + 15y = 21 + 11[/tex]

   [tex]\rm :\longmapsto\:(15x + 17x) + (17y + 15y) = 32[/tex]

   [tex]\rm :\longmapsto\:32x + 32y = 32[/tex]

   [tex]\rm :\longmapsto\:32(x + y) = 32[/tex]

   [tex]\bf\implies \:x + y = 1[/tex]

   [tex]\overbrace{ \underline { \boxed { \bf \therefore \: The \: value \: of \: x + y \: is \:1}}}[/tex]

   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.

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