Question

Solve the simultaneous equations

Answer 1

Answer:

Step-by-step explanation:

Equation 1:     2x + 3y = 8

Equation 2:     3x + 2y = 7

Step 1: Multiply each equation by a suitable number so that the two equations have the same leading coefficient. An easy choice is to multiply Equation 1 by 3, the coefficient of x in Equation 2, and multiply Equation 2 by 2, the x coefficient in Equation 1:

   

3 * (Eqn 1) --->      

3* (2x + 3y = 8)

--->    6x + 9y = 24  

2 * (Eqn 2) --->      

2 * (3x + 2y = 7)

--->    6x + 4y = 14         Both equations now have the same leading coefficient = 6

 

Step 2: Subtract the second equation from the first.

          -(6x + 9y = 24

          -(6x + 4y = 14)

           

                    5y = 10

Step 3: Solve this new equation for y.

                    y = 10/5 = 2

Step 4: Substitute y = 2 into either Equation 1 or Equation 2 above and solve for x. We'll use Equation 1.

          2x + 3(2) = 8  

          2x + 6 = 8 Subtract 6 from both sides

          2x = 2 Divide both sides by 2

          x = 1  

Solution: x = 1, y = 2 or (1,2).