Question

To solve the system of linear equations 3 x + 5 y = 2 and 6 x + 10 y = 8 by using the linear combination method, Laura correctly multiplied the first equation by –2 to get Negative 6 x minus 10 y = negative 4 and then correctly added the equations Negative 6 x minus 10 y = negative 4 and 6 x + 10 y = 8 to get 0 = 4. How many solutions are there to the system of equations?

0
1
2
4

Answer 1

x = 1

y = 1/5

Explanation:

Given the system of linear equations

x + 5 y = 2 .... 1 ×2

6 x + 10 y = 8 .... 2×1

___,_______

2x+10y = 4

6x+10y = 8

Subtract

2x-6x = 4-8

-4x = -4

x = 1

Substitute x =1 into 1

x+5y = 2

1+5y = 2

5y = 2-1

5y = 1

y = 1/5

Hence the solution to the system of equation is (1, 1/5)