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2 years ago

Solve the system by substitution

Mathematics

1 answer:

kumpel [21]2 years ago

6 0

<h3>Answer:</h3>

(x, y) = (1, 4)

<h3>Step-by-step explanation:</h3>

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.

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