Question

Solve by Substitution method 5x + 2y = 23, 3x - 5y = -11​

Answer 1

Answer:

Break down the problem into these 2 equations.

5 x + 2 y=23

5X + 2 y = 3 x-5y

Solve the 1st equation:

5X + 2 y =23

x=23 - 2 y

-----------

2

Solve the 2nd equation:

5 x + 2 y= 3 x - 5 y.

7y

x= - ____

2

Collect all solutions.

x=23-2y 7y

____,-___

5. 2

Answer 2

       $\underline{\bold{Answer:}}$

       $x = 3, y = 4$

       $\underline{\bold{Explaination:}}$

       $\text{The two equations are: }$

       $\boxed{5x + 2y = 23}\text{------(i)}$

       $\boxed{3x - 5y = -11}\text{------(ii)}$

       $\text{In (i)}$

       $\boxed{5x + 2y = 23}$

       $\text{Transposing }2y \text{ to R.H.S}$

$\implies \boxed{5x = 23 - 2y}$

       $\text{Transposing }5 \text{ to R.H.S}$

$\implies \boxed{x = \frac{23 - 2y}{5}}$

       $\text{Substituting the value of }x \text{ in (ii)}$

$\implies \boxed{3(\frac{23 - 2y}{5}) - 5y = -11}$

       $\text{Simplifying the equation}$

$\implies \boxed{\frac{69 - 6y}{5} - 5y = -11}$

       $\text{Simplifying the equation}$

$\implies \boxed{\frac{69 - 6y-25y}{5} = -11}$

       $\text{Simplifying the equation}$

$\implies \boxed{\frac{69 - 31y}{5} = -11}$

       $\text{Transposing }5 \text{ to R.H.S}$

$\implies \boxed{69 - 31y= (5)(-11)}$

       $\text{Simplifying the equation}$

$\implies \boxed{69 - 31y= -55}$

       $\text{Transposing }69 \text{ to R.H.S and simplifying the equation}$

$\implies \boxed{ - 31y= -124}$

       $\text{Transposing }31 \text{ to R.H.S and simplifying the equation}$

$\implies \boxed{y = 4}$

       $\text{Substituting the value of }y \text{ in (i)}$

$\implies \boxed{5x + 2(4) = 23}$

       $\text{Simplifying the equation}$

$\implies \boxed{5x + 8 = 23}$

       $\text{Transposing }8 \text{ to R.H.S and simplifying the equation}$

$\implies \boxed{5x = 15}$

       $\text{Transposing }5 \text{ to R.H.S and simplifying the equation}$

$\implies \boxed{x = 3}$