Answer:
1. Consistent equations
x + y = 3
x + 2·y = 5
2. Dependent equations
3·x + 2·y = 6
6·x + 4·y = 12
3. Equivalent equations
9·x - 12·y = 6
3·x - 4·y = 2
4. Inconsistent equations
x + 2 = 4 and x + 2 = 6
5. Independent equations
y = -8·x + 4
8·x + 4·y = 0
6. No solution
4 = 2
7. One solution
3·x + 5 = 11
x = 2
Step-by-step explanation:
1. Consistent equations
A consistent equation is one that has a solution, that is there exist a complete set of solution of the unknown values that resolves all the equations in the system.
x + y = 3
x + 2·y = 5
2. Dependent equations
A dependent system of equations consist of the equation of a line presented in two alternate forms, leading to the existence of an infinite number of solutions.
3·x + 2·y = 6
6·x + 4·y = 12
3. Equivalent equations
These are equations with the same roots or solution
e.g. 9·x - 12·y = 6
3·x - 4·y = 2
4. Inconsistent equations
Inconsistent equations are equations that are not solvable based on the provided set of values in the equations
e.g. x + 2 = 4 and x + 2 = 6
5. Independent equations
An independent equation is an equation within a system of equation, that is not derivable based on the other equations
y = -8·x + 4
8·x + 4·y = 0
6. No solution
No solution indicates that the solution is not in existence
Example, 4 = 2
7. One solution
This is an equation that has exactly one solution
Example 3·x + 5 = 11
x = 2
Answer:
x=-16/3 (-5.33)
Step-by-step explanation:
3(x-2)+4x=10(x+1)
3x-6+4x=10x+10
7x-6=10x+10
-6-10=10x-7x
-16=3x
x=-16/3
Answer:
x = 15
Step-by-step explanation:
angles 2 and 4 are supplementary so they add up to 180
2x + 10 + 4x + 80 = 180
6x + 90 = 180
6x = 90
x = 15
If a graph is proportional then the line will go through the origin at point (0, 0). If the equation is proportional then it will be in the form of y=kx with no other operations after. The constant of proportionality is another way to say the slope and in your specific equation the slope would be 1/5.
It's simple math, but if you don't understand, we can help. To begin with, you must first convert 2 1/4 to an improper fraction. You'd be left with 9/4 after the conversion. Write out 9/4 ÷ 5/8. After doing so, find the reciprocal of 5/8 (switch the numerator and the denominator). Now, write out the question as 9/4 × 8/5. Multiply straight across, as you do not need common denominators when multiplying or dividing fractions. Your final answer should be 72/20. When simplified, you should get 3 2/20, or when simplified to the smallest amount, 3 1/10. Hope I was clear enough to help! :)
