Solve 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)
To solve the system of equations using the substitution method, we'll solve one equation for either variable and substitute it into the other equation.
Let's solve the first equation for x:
2x - y = -4
Adding y to both sides:
2x = y - 4
Dividing both sides by 2:
x = (y - 4)/2
Now, we'll substitute this expression for x into the second equation:
-5x + 3y = 14
Substituting x with (y - 4)/2:
-5((y - 4)/2) + 3y = 14
Expanding and simplifying:
(-5/2)(y - 4) + 3y = 14
(-5/2)y + 10 + 3y = 14
(-5/2)y + 3y = 14 - 10
(-5/2)y + 6y/2 = 4/2
(-5 + 6/2)y = 4/2
(-5 + 3)y = 2
-2y = 2
y = -1
Now that we have the value of y, we can substitute it back into either equation to find x. Let's substitute it into the first equation:
2x - (-1) = -4
2x + 1 = -4
2x = -5
x = -5/2
Therefore, the solution to the system of equations is (-5/2, -1) or (-2.5, -1).