Jerry solved the system of equations.
x minus 3 y = 1. 7 x + 2 y = 7.
As the first step, he decided to solve for y in the second equation because it had the smallest number as a coefficient. Max told him that there was a more efficient way. What reason can Max give for his statement?
The variable x in the first equation has a coefficient of one so there will be fewer steps to the solution.
The variable x in the second equation has a coefficient of 7 so it will be easy to divide 7 by 7.
The variable y in the second equation has a coefficient of 2 so it will be easy to divide the entire equation by 2.
The variable x in the second equation has the largest coefficient. When dividing by 7, the solution will be a smaller number.
The variable x in the first equation has a coefficient of one so there will be fewer steps to the solution.
In the system of equations, which variable would it be easiest to solve for?
2 x + 4 y = 26. 3 x + y = 9.
The easiest to solve for is x in the first equation.
The easiest to solve for is y in the first equation.
The easiest to solve for is x in the second equation.
The easiest to solve for is y in the second equation.
The easiest to solve for is y in the second equation.
Which shows the correct first step to solving the system of equations in the most efficient manner?
3 x + 2 y = 17. x + 4 y = 19.
x = negative 4 y + 19
x = StartFraction negative 2 y + 17 Over 3 EndFraction
4 y = negative x + 19
y = StartFraction negative 3 x + 17 Over 2 EndFraction
x = StartFraction negative 2 y + 17 Over 3 EndFraction
Max can give the reason that the variable x in the first equation has a coefficient of one, so there will be fewer steps to the solution.
Max can give the reason that the variable x in the first equation has a coefficient of one, which means that there will be fewer steps to the solution.
When we want to solve a system of equations, it is often more efficient to start by eliminating one variable. In this case, Jerry chose to solve for y in the second equation because it had the smallest number as a coefficient. However, Max can argue that starting with the first equation, which has x with a coefficient of one, would lead to a more straightforward solution.
By rearranging the first equation, we can isolate x:
x - 3y = 1
x = 1 + 3y
Now we substitute this expression for x in the second equation:
7(1 + 3y) + 2y = 7
Simplifying the equation gives us:
7 + 21y + 2y = 7
23y = 0
Dividing both sides of the equation by 23, we find that y = 0.
Then, substituting this value of y into the first equation, we can find x:
x - 3(0) = 1
x = 1
Therefore, the solution to the system of equations is x = 1 and y = 0.
By starting with the equation where x has a coefficient of one, we were able to solve for y in just one step. This demonstrates the efficiency of Max's approach.