When is the substitution method a better method than graphing for solving a system of linear equations?
what is the Solving Systems Using Substitution quick check answers?
The substitution method is a better method than graphing for solving a system of linear equations in the following scenarios:
1. When the equations have variables with coefficients that are fractions or decimals: Substitution often involves simpler arithmetic calculations compared to graphing, especially when dealing with fractions or decimals.
2. When the equations have variables with coefficients that are not easily graphable: Graphing becomes difficult when the coefficients of variables are not integers, making substitution a more convenient method.
3. When the system involves more than two equations: Graphing becomes increasingly complex as the number of equations increases, while substitution remains a manageable process regardless of the number of equations.
4. When precision and accuracy are crucial: Substitution allows for exact solutions, while graphing may introduce potential errors due to reading values off the graph, especially if it is not accurately plotted.
5. When the equations have variables that can easily be solved algebraically: Substitution is more favorable when the equations involve variables that can be easily isolated. It enables direct substitution of one equation into the other, resulting in a simpler process than graphing.
In summary, the substitution method is often preferable to graphing when dealing with equations that have non-integer coefficients, complex or numerous equations, a need for precise solutions, or variables that can be easily isolated algebraically.
The substitution method is a better method than graphing for solving a system of linear equations under certain circumstances. In general, the substitution method is advantageous when:
1. The equations involve fractions or decimals: Graphing can be challenging when dealing with complex numbers, leading to inaccurate or imprecise solutions. On the other hand, the substitution method allows us to work with exact values, making it easier to handle fractions or decimals.
2. The system involves equations with variables that have coefficients that are difficult to graph: For example, if one of the equations has coefficients like 3/7 or -5/6, it may be challenging to construct an accurate graph. Solving the equations using substitution allows us to avoid the complexities that arise from graphing such coefficients.
3. Higher precision is required: Graphing provides a visual representation of the solution(s) but is limited in terms of precision. For more precise answers, the substitution method is preferable as it allows for exact solutions without any rounding errors.
4. Fewer computational resources are available: Graphing requires graph paper, a graphing calculator, or computer software. On the other hand, solving equations using the substitution method only requires basic arithmetic operations, making it accessible to everyone, even without advanced computational resources.
To summarize, the substitution method is a better choice than graphing for solving a system of linear equations when dealing with fractions, decimals, complex coefficients, or when higher precision is required. Additionally, it is a more accessible method that doesn't rely on specialized tools or resources.
If one of the equation is in the form y = ....
or x = .... , or can easily be changed to one of those forms, I would use substitution
e.g
3x + 4y = 36
y = 2x+3
definitely use substitution