Question

one equation in a system of equations is ( y = 2x + 4 ). which of the following would be the second equation so that the system has ( (1, 6) ) as its only solution?
a ( y = -2(x + 2) )
b ( y = 4x - 7 )
c ( y = 2x + 8 )
d ( y = 5x + 1 )

Explanation:

Step1: Test point (1,6) in Option A

Substitute $x=1, y=6$ into $y=-2(x+2)$:
$6=-2(1+2)=-6$ → False

Step2: Test point (1,6) in Option B

Substitute $x=1, y=6$ into $y=4x-7$:
$6=4(1)-7=-3$ → False

Step3: Test point (1,6) in Option C

Substitute $x=1, y=6$ into $y=2x+8$:
$6=2(1)+8=10$ → False

Step4: Test point (1,6) in Option D

Substitute $x=1, y=6$ into $y=5x+1$:
$6=5(1)+1=6$ → True

Step5: Check line uniqueness

The given line $y=2x+4$ has slope 2; Option D has slope 5 (different slopes, so lines intersect at exactly one point, (1,6)).

Answer:

D. $y = 5x + 1$