Question

olve the following system using the substitution method.

2x−y=−4
−5x+3y=14
(1 point)
Responses

(−1, 3)
(−1, 3)

(1,6)
open paren 1 comma 6 close paren

(2,8)
open paren 2 comma 8 close paren

(3,5)

Answer 1

To solve the system using the substitution method, we start by solving one of the equations for one variable and then substitute this expression into the other equation.

From the first equation, we can solve for x in terms of y:

2x - y = -4
2x = y - 4
x = (y - 4)/2

Now substitute this expression for x into the second equation:

-5((y - 4)/2) + 3y = 14
-5(y - 4) + 6y = 28
-5y + 20 + 6y = 28
y + 20 = 28
y = 8

Substitute this value for y back into the expression for x:

x = (8 - 4)/2
x = 4/2
x = 2

Therefore, the solution to the system is (2, 8).