SOLUTION: Determine whether each order pair is solution of the system of the system of linear equations { 3y=9x+6 { 3x-y=-2 a)(-2,-4) b)(0,-2) A)IS (-2,-4) A SOLUTION? YES OR NO

Algebra ->  Finance -> SOLUTION: Determine whether each order pair is solution of the system of the system of linear equations { 3y=9x+6 { 3x-y=-2 a)(-2,-4) b)(0,-2) A)IS (-2,-4) A SOLUTION? YES OR NO      Log On


   

Question 918635: Determine whether each order pair is solution of the system of the system of linear equations
{ 3y=9x+6
{ 3x-y=-2
a)(-2,-4)
b)(0,-2)

A)IS (-2,-4) A SOLUTION? YES OR NO
B)IS (0,-2) A SOLUTION? YES OR NO
Found 2 solutions by ewatrrr, MathLover1:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi

Try the ordered pair (x,y) values given for the Points in the Simplest EQ

3x-y = -2

YES(-2,-4),  3(-2)-(-4) = -2

NO!(0,-2),   0 -(-2)  = 2  ≠  -2

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
+3y=9x%2B6.......eq.1
+3x-y=-2.......eq.2
__________________________

a)
if (-2,-4)
3y=9x%2B6.......eq.1
+3%28-4%29=9%28-2%29%2B6.......eq.1
+-12=-18%2B6
+-12=-12 ....true; so (-2,-4) is a solution for eq.1

+3x-y=-2.......eq.2
+3%28-2%29-%28-4%29=-2
+-6%2B4=-2
+-2=-2........true; so (-2,-4) is a solution for eq.2
__________________________

b)
if (0,-2)


+3%28-2%29=9%280%29%2B6.......eq.1
+-6=0%2B6
+-6=-12 ....not true; so (0,-2) is not a solution for eq.1

+3x-y=-2.......eq.2
+3%280%29-%28-2%29=-2
+0%2B2=-2
+2=-2........not true; so (0,-2) is not a solution for eq.2
__________________________


A)IS (-2,-4) A SOLUTION? YES
B)IS (0,-2) A SOLUTION? +NO
we will graph both lines and see if given points lie on lines:
first line +3y=9x%2B6.......eq.1 we can simplify it dividing both sides by 3
+y=3x%2B2.......eq.1 compare to +3x-y=-2.......eq.2=>
+3x%2B2=y.......eq.2 and we see it's same
that means the two lines are identical (one lies perfectly on top of the other) and intersect at all points of both lines