Systems of linear equations can be used to solve many, but not all, real-world problems. When you chose the problem for your journal entry, how did you know that this problem could be solved using a system of linear equations? What specific characteristics does your problem have that made it a good choice? List at least three reasons why the problem you described in your journal prompt can be solved using a system of linear equations.
When choosing a problem for my journal entry, I considered the following characteristics that indicated it could be solved using a system of linear equations:
1. Linearity: Linear equations have variables raised to the power of 1 and are expressed as linear functions. If the problem involves a relationship that is linear, such as a straight line, it is likely solvable using a system of linear equations. For example, if I am given the cost of apples and oranges and asked to find the number of each type of fruit purchased, the relationship between cost and quantity is linear.
2. Consistent Variables: A problem that involves multiple variables with consistent relationships often lends itself to a system of linear equations. For instance, if I am given measurements of the sides of a rectangle and asked to find its area and perimeter, the variables (length and width) have consistent relationships that can be represented by a system of linear equations.
3. Simultaneous Constraints: If a problem has multiple constraints or conditions that need to be satisfied simultaneously, a system of linear equations is a suitable approach. For example, if I am given the ages of three people and asked to find their current ages based on the information that the sum of their ages is 90 and the oldest person is twice as old as the youngest, a system of linear equations can handle these simultaneous conditions.
In summary, a problem can be solved using a system of linear equations when it exhibits linearity, consistent variables with relationships, and simultaneous constraints. These characteristics allow us to represent the problem mathematically and solve for the unknown variables using systems of equations.
Select the correct answer from the list.(1 point)
Evidence must be ____ and _____for it to be considered effective in supporting a claim.
The correct answer from the list is:
- Relevant and credible
Evidence is relevant if it(1 point)
Responses
provides enough evidence to support the claim.
is directly related to the claim.
provides a personal experience related to the claim.
is taken entirely from an online source.
The correct answer is:
- is directly related to the claim.
Which of the following describes a claim?(1 point)
Responses
a statement that will grab the audience's attention
a statement that everyone in the audience will agree with
a statement that connects evidence to a reason
a statement that presents the speaker’s position or opinion
The correct answer is:
- a statement that presents the speaker’s position or opinion