Question

Solve the following pair of linear equations by the substitution and cross-multiplication
methods..
(i) 4x-3y=23 , 3x+4y=11​

Answer 1

Answer:

Step-by-step explanation:

4x+3y=11

by cross multiplying

11(_3x+4y)=23(4x+3y)

_33x+44y=92x+69y

_33x_92x=69y_44y

_125x=25y

y=_125x/25=_5x

y=_5x substitute in (1)equation

_3x+4(_5x)_23=0

_3x_20x_23=0

Answer 2

Step-by-step explanation:

Step by Step Solution

System of Linear Equations entered :  [1] 4x - 3y = 23   [2] 3x + 4y = 11 Graphic Representation of the Equations : -3y + 4x = 23 4y + 3x = 11 Solve by Substitution :

// Solve equation [2] for the variable  y 

 

[2] 4y = -3x + 11 [2] y = -3x/4 + 11/4

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

  [1] 4x - 3•(-3x/4+11/4) = 23   [1] 25x/4 = 125/4   [1] 25x = 125

// Solve equation [1] for the variable  x 

  [1] 25x = 125    [1] x = 5 

// By now we know this much :

  x = 5   y = -3x/4+11/4

// Use the  x  value to solve for  y 

  y = -(3/4)(5)+11/4 = -1 

Solution :

 {x,y} = {5,-1}