Question

PLEASE HELP ME!!!!!!!!!

Answer 1

Answer:

  (a)  (5, -3)

Step-by-step explanation:

The "substitution method" for solving a system of equations requires that you write an expression that can be substituted for a variable in one or more of the other equations in the system.

Expression to substitute

The given equations are ...

• y = x -8
• 2x +3y = 1

We notice the first equation gives an expression for y. This is exactly what we want to substitute for y in the second equation.

Substitution

When the expression (x-8) is substituted for y in the second equation, you get ...

  2x +3(x -8) = 1

This simplifies to ...

  5x -24 = 1

Solution

This 2-step equation can now be solved in the usual way:

  5x = 25 . . . . . . add 24 to isolate the variable term

  x = 25/5 = 5 . . . . . divide by the coefficient of x

Note that we now know what the correct answer choice is.

Using the expression for y, we find ...

  y = x -8 = 5 -8 = -3

The solution is (x, y) = (5, -3).

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The attached graph confirms this solution.