Find the solution to the system of equations by substitution.
-
A) (5, 2)
B) (-5, -2)
C) (-5, 2)
D) (5, -2)

Question

Find the solution to the system of equations by substitution.
-
A) (5, 2) 
B) (-5, -2) 
C) (-5, 2) 
D) (5, -2)

Quizplus · Accepted Answer

Looking at the second equation, we can solve for y in terms of x:
3x + 4y = 14
4y = -3x + 14
y = (-3/4)x + 14/4
y = (-3/4)x + 7/2

Now we can substitute this expression for y into the first equation:
x + 2y = -6
x + 2((-3/4)x + 7/2) = -6
x - (3/2)x + 7 = -6
-(1/2)x = -13
x = 26

Substituting x = 26 into our expression for y:
y = (-3/4)(26) + 7/2
y = -39/4 + 14/4
y = -25/4

Thus, the solution to the system of equations is (26, -25/4), which is closest to (5, -2). Therefore, the best choice is D.

Find the Solution to the System of Equations by Substitution