Using elimination method, simultaneously solve this equation: 2y+3x=7 and 4x+3y=15

Answer: x = - 9, y = 14

Step-by-step explanation:

3x + 2y = 7 ... equation 1

4x + 3y = 15 ... equation 2

Solving using elimination method, we have to decide the variable we are eliminating first, we could eliminate x or y. If we are to eliminate y first, we will multiply equation 1 by 3 and equation 2 by 2 so that the coefficient of y can be the same. The equation then becomes

3 (3x + 2y = 7)

2 (4x + 3y = 15)

Expanding, we have

9x + 6y = 21 ... equation 3

8x + 6y = 30 ... equation 4

Now that the coefficient of y is the same, we will subtract equation 4 from equation 3 to eliminate y, we have

x = - 9

Substitute y = - 9 into equation 1 to find the value of x, we have:

3 (-9) + 2y = 7

-27 + 2y = 7

2y = 7 + 27

2y = 34

y = 34/2

y = 14