Answer:
- order pair of [tex]3x+2y=6[/tex] is (0,3)
- order pair of [tex]-5x+y=-10[/tex] is (1,-5)
- order pair of [tex]x-4y=8[/tex] is (4,-1)
- order pair of [tex]-6x-5y=30[/tex] is (0,-6)
Step-by-step explanation:
We need to fill the box with each equation to the ordered pair that represents one of its solutions.
The given equations are :
A) [tex]3x+2y=6[/tex]
B) [tex]-5x+y=-10[/tex]
C) [tex]x-4y=8[/tex]
D) [tex]-6x-5y=30[/tex]
Ordered pair are:
(0, -6) , (0,3) , (4,-1) ,(1,-5)
We will check correct order pair by plunging in each equation
Put (0, -6) In [tex]3x+2y=6[/tex]
[tex]3(0)+2(-6) = 6[/tex]
[tex]-12 ≠ 6[/tex]
Now, Put (0,3) In [tex]3x+2y=6[/tex]
[tex]3(0)+2(3) = 6[/tex]
[tex]6 = 6[/tex]
Hence, correct order pair of [tex]3x+2y=6[/tex] is (0,3) .
Put (0, -6) In [tex]-5x+y=-10[/tex]
[tex]-5(0) + (-6)= -10[/tex]
[tex]-6 ≠ -10[/tex]
Now, Put (4,-1) In [tex]-5x+y=-10[/tex]
[tex]-5(4) + (-1)= -10[/tex]
[tex]-20 + (-1)= -10[/tex]
[tex]-21 ≠ -10[/tex]
Now, Put (1,-5) In [tex]-5x+y = -10[/tex]
[tex]-5(1) + (-5)= -10[/tex]
[tex]-10 = -10[/tex]
Hence, correct order pair of [tex]-5x+y=-10[/tex] is (1,-5) .
Put (0, -6) In[tex]x-4y=8[/tex]
[tex](0)-4(-6)=8[/tex]
[tex]-24 ≠ -10[/tex]
Now, put (4, -1) In[tex]x-4y=8[/tex]
[tex](4)-4(-1)=8[/tex]
[tex](4)+4=8[/tex]
[tex]8 =8[/tex]
Hence, correct order pair of [tex]x-4y=8[/tex] is (4,-1) .
we left with one orderpair and equation so,
Check (0, -6) for [tex]-6x-5y=30[/tex]
[tex]-6(0)-5(-6)=30[/tex]
[tex]30=30[/tex]
Hence, correct order pair of [tex]-6x-5y=30[/tex] is (0,-6) .
The correctly match solution is mention in figure-1