Question

2x+3y=8;3x+2y=7 substitution method

Answer 1

Answer:

These are simultaneous equations. To solve them, we need to do something to these equations to that either the coefficents of x or y are the same. So multiply each equation by a suitable number, a good choice is to multiply Equation 1 by 3, and multiply Equation 2 by 2, which means in both of the equations the coefficient is 6. Next we subtract the second equation from the first, because we want to eliminate the "x" values in each equation leaving us only with y. Then we solve this new equation for y. Next we substitute y = 2 into either Equation 1 or Equation 2 above and solve for x.

Answer 2

Given :

• 2x + 3y = 8
• 3x + 2y = 7

To Find :

• Value of x and y by substitution method.

Solution :

2x + 3y = 8 - (1)

3x + 2y = 7 - (2)

From equation (1), we get :

$\sf : \implies 2x + 3y = 8$

$\sf : \implies 2x = 8 - 3y$

$\sf : \implies x = \dfrac{8-3y}{2}$

Substitute it in equation (2) :

$\sf : \implies 3\Bigg( \dfrac{8-3y}{2}\Bigg) + 2y = 7$

$\sf : \implies \dfrac{24-9y}{2} + 2y = 7$

$\sf : \implies \dfrac{24-9y}{2} + \dfrac{4y}{2} = 7$

$\sf : \implies \dfrac{24-9y + 4y}{2} = 7$

$\sf : \implies \dfrac{24-5y}{2} = 7$

$\sf : \implies 24-5y = 7 \times 2$

$\sf : \implies 24-5y = 14$

$\sf : \implies -5y = 14-24$

$\sf : \implies -5y = -10$

$\sf : \implies 5y = 10$

$\sf : \implies y = \cancel{\dfrac{10}{5}}$

$\sf : \implies y = 2$

$\large \underline{\boxed{\bf{y = 2}}}$

Now, substitute value of y in equation (1) :

$\sf : \implies 2x + 3(2) = 8$

$\sf : \implies 2x + 6 = 8$

$\sf : \implies 2x = 8 - 6$

$\sf : \implies 2x = 2$

$\sf : \implies x = \cancel{\dfrac{2}{2}}$

$\sf : \implies x = 1$

$\large \underline{\boxed{\bf{x = 1}}}$

Hence, value of :

• x = 1
• y = 2