Answer:
Lines A and B form a consistent independent system
Step-by-step explanation:
we know that
A consistent system of equations has at least one solution
In this problem
The system of Line A and Line B has only one solution, since it has only one point of intersection.
and the Line A is different to Line B
therefore
Lines A and B form a consistent independent system
(independent because Lines A and B are different)
The small dish costs $2 each and the large dish costs $4 each,
2(3)+4(2)=6+8=14
2(4)+4(1)=8+4=12
Answer:
The larger number is -6, the smaller number is -15
Step-by-step explanation:
We have two numbers, a and b.
We know that one number is larger than another by 9.
Then we can write:
a = b + 9
then a is larger than b by 9 units.
If the greater number is increased by 10 (a + 10) and the lesser number is tripled (3*b), the sum of the two would be -41:
(a + 10) + 3*b = -41
So we got two equations:
a = b + 9
(a + 10) + 3*b = -41
This is a system of equations.
One way to solve this is first isolate one variable in one of the two equations:
But we can see that the variable "a" is already isolated in the first equation, so we have:
a = b + 9
now we can replace that in the other equation:
(a + 10) + 3*b = -41
(b + 9) + 10 + 3*b = -41
now we can solve this for b.
9 + b + 10 + 3b = -41
(9 + 10) + (3b + b) = -41
19 + 4b = -41
4b = -41 -19 = -60
b = -60/4 = -15
b = -15
then:
a = b + 9
a = -15 + 9 = -6
a = -6
Answer:
7 + 8 = 7 + 7 + 1.
Step-by-step explanation:
We know that, 'double plus one facts' is used to make the addition of numbers easy.
For e.g. we have 8 + 9 = 17. This addition can also be done as 8 + 8 + 1 = 17 i.e. we write first term twice and add 1 to get the result.
Hence, we give the name to this type of addition as 'double plus one'.
Now, we have to use this fact for 7 + 7.
So, we consider 7 + 8 = 15.
Therefore, 7 + 8 can be written as 7 + 7 + 1
Hence, the double plus one facts for 7 + 7 is 7 + 8 = 7 + 7 + 1.
