Question

2x+5y=24 x+4y=15 if (x,y) satisfies the system of equations above, what is the value of x+y? Explain your answer step by step

Answer 1

9

Explanation:

these system of equations has an intersection point of (x,y) meaning they are equal

1. 2x + 5y = 24

2. x + 4y = 15

if we multiply the second equation by 2, the x values will be equal in both equations and cancel them out :

2(x + 4y = 15) ->> 2x + 8y = 30

1. 2x + 5y = 24

2.2x + 8y = 30

____________ subtract

2x - 2x = 0

5y - 8y = -3y

24 - 30 = -6

0 + -3y = -6

y = 2

substitute y as 2 to find x value

1. 2x + 5(2) = 24

2x + 10 = 24

2x = 14

x = 7

2. x + 4(2) = 15

x + 8 = 15

x = 7

x= 7, y = 2

x+y = 7+2 = 9