Question

3x+2y=53 and 2x+3y=47 by substitution method

Answer 1

Answer:

The solution is (x, y) = (- 13, 46)

Step-by-step explanation:

Substitution Method :-

1. Solve one of the equations for either x = or y = .
2. Substitute the solution from step 1 into the other equation.
3. Solve this new equation.
4. Solve for the second variable.
5. Step 1: Solve one of the equations for either x = or y = .

Given equations are 3x+2y=53 and 2x+3y=47

           3x+2y=53            ................................................. ( 1 )

          2x+3y=47             ..................................................( 2 )

Step 1: Solve one of the equations for either x = or y = . We will solve first equation for y.

3x + 2y = 53

subtract 3x from the sides of above equation,

2y = 53 - 3x

y = $\frac{53 - 3x}{2}$

Step 2: Substitute the solution from step 1 into the second equation.

Put value of y in equation (2),

2x + 3y = 47

2x + 3 ($\frac{53 - 3x}{2}$) = 47

2x + ($\frac{159 - 9x}{2}$) = 47

Step 3: Solve this new equation.

Multiply by 2 on both the sides in above equation,

4x + 159 - 9x = 94

159 - 5x = 94

subtract by 159 on both the sides in above equation,

159 - 5x -159 = 94 - 159

- 5x = 65

divide both the sides by -5 in above equation,

x = - 13

Step 4: Solve for the second variable

Put x = - 13 in y = $\frac{53 - 3x}{2}$

$y\,=\,\frac{53 + 39}{2}$

$y\,=\,\frac{92}{2}$

$y\,=\,46$

The solution is: (x, y) = (- 13, 46)