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.
