3. Which method would be the simplest way to solve the system?
y =1/2 x
2x + 3y = 28
A.) graphing
B.) substitution
C.) elimination
D.) distributive
I think it is B.
I agree.
Me too
To determine the simplest way to solve the system of equations, let's consider the available methods:
A.) Graphing: This method involves graphing both equations on the same coordinate plane and finding the point of intersection. While it is a valid approach, it may not be the simplest way in this case.
B.) Substitution: This method involves solving one equation for a variable and substituting it into the other equation. This can simplify the system and lead to finding the solution. This could be an appropriate approach, but let's consider the other options as well.
C.) Elimination: This method involves manipulating the equations to eliminate one variable when added or subtracted. This can simplify the system and lead to finding the solution. This could also be a valid approach.
D.) Distributive: The distributive property is a mathematical rule used to simplify expressions, but it is not specifically a method for solving systems of equations.
Now, let's analyze the given system of equations:
y = (1/2)x and 2x + 3y = 28
Both equations appear to be already solved for y. Therefore, you are correct. The simplest method for solving this particular system would be through substitution (option B), as you can directly substitute the y-value in the first equation into the second equation.
Great job!
To determine which method would be the simplest way to solve the given system, let's take a look at the options provided and assess the situation.
A.) Graphing: This method involves graphing both equations on a coordinate plane and finding the point of intersection. While this can be an effective method, it may not always be the simplest, especially if the equations have fractions or decimals.
B.) Substitution: This method involves solving one equation for one variable and then substituting that expression into the other equation. This can be a good option when one equation is already solved for a variable, making substitution straightforward.
C.) Elimination: This method involves adding or subtracting the equations in such a way that one variable is eliminated, allowing for the solution of the remaining variable. This method is most useful when the coefficients of one of the variables are opposites or have a straightforward ratio.
D.) Distributive: This is not a method for solving a system of equations. The distributive property is a mathematical property used in simplifying expressions.
Now, let's apply the options to the given system of equations:
y = (1/2)x
2x + 3y = 28
In this case, option B, substitution, would indeed be the simplest method. By solving the first equation for y, which already gives it in terms of x, we can substitute the expression (1/2)x for y in the second equation, simplifying it to a single-variable equation in terms of x. Then, solving for x will allow us to find the value of y.
So, your answer, B.) substitution, is correct.