Look at the system of equations below.
4x-5y=3
3x+5y=13

a student makes this argument: elimination is the best method for solving this system because the y-coefficient in the first equation is the opposite of the y-coefficient in the second equation.

complete the student’s argument by explaining why substitution and graphing are less efficient methods than elimination for this system.

The substitution and graphing methods are less efficient methods than elimination method for this system as there is extra amount of steps we have to take to solve the same system of equations 4x-5y=3  , 3x+5y=13

We have equations

4x-5y=3  ... (1)

3x+5y=13 ...(2)

Substituting the value of 5y = 13-3x from equation (2) into equation(1)

4x-(13-3x)=3

4x-13+3x=3

7x= 3+13

7x= 16

x =

Substitute the value of x = in y value, we get

4x-5y=3

3x+5y=13

Adding both the equations, we get

Put the value of x in any one of the above equation, we get

So, the Elimination method is the best method for solving this system because the y-coefficient in the first equation is the opposite of the y-coefficient in the second equation and it is less time consuming.

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