Question

What is the solution to the system of equations using the linear combination method {4x+y=5, 3x+y=8?

Answer 1

4x + y = 5
3x + y = 8
y = -3x + 8

4x +(-3x + 8) = 5
4x -3x + 8 = 5
x + 8 = 5
x = -3

y = -3(-3) + 8
y = -9 + 8
y = -1

Answer 2

x = -3 and y = 17

Explanation:

The given system of equations is

4x + y = 5 --------(1)

and 3x + y = 8 ----------(2)

Now we subtract equation (2) from equation (1)

(4x+y) - (3x+y) = 5 - 8

(4x - 3x) + (y-y) = -3

x = -3

Now we put x = -3 in equation (1)

4(-3) + y = 5

-12 + y = 5

y = 5 + 12 = 17

Therefore, x = -3 and y = 17 is the solution of the given system of equations.