Question

Solve the system by substitution

Answer 1

Answer:

  (x, y) = (1, 4)

Step-by-step explanation:

Given:

• -4.5x-2y=-12.5
• 3.25x-y=-0.75

Find:

  x and y using the method of substitution

Solution:

To solve a system of equations by substitution, you find an expression for one of the variables in terms of the others, then substitute that wherever that variable is used*. Usually, you choose one of the equations to solve for the variable you're going to substitute for, then you make the substitution into the remaining equation(s).

Since the coefficient of y in the second equation is -1, it is convenient to solve for y in that equation, then use the resulting expression to substitute for y in the first equation.

  3.25x = y - 0.75 . . . . . . add y

  3.25x + 0.75 = y . . . . . . add 0.75

Using this expression in place of y in the first equation, we have ...

  -4.5x -2(3.25x +0.75) = -12.5

  -11x -1.5 = -12.5 . . . . . . . simplify

  -11x = -11 . . . . . . . . . . . . . add 1.5

  x = 1 . . . . . . . . . . . . . . . . . divide by -11

We can substitute this value into the equation we have for y:

  y = 3.25x +0.75 = 3.25·1 + 0.75

  y = 4

The solution to the system of equations is (x, y) = (1, 4).

_____

* There's no point in substituting for the variable in the equation you used to find the expression. It will give you no useful information. Here, that would look like ...

  3.5x -(3.5x+0.75) = 0.75 . . . . . . . . substitute for y in the second equation

  0.75 = 0.75 . . . . . . . always true. Not a useful substitution.