Question

Use substitution to solve the system of linear equations. In your final answer, include all of your work. y = -3x + 4 and x + 1/3y = 4/3

Answer 1

Answer:

y = -3x +4

Step-by-step explanation:

Using the expression for y, we can substitute that into the second equation:

... x + (1/3)(-3x +4) = 4/3

... 4/3 = 4/3 . . . . . simplify (True for any value of x.)

These equations are dependent and have an infinite number of solutions.

Answer 2

Answer:  The system has an infinite number of solutions.

Step-by-step explanation:  We are given to use the substitution method to solve the following system of linear equations :

$y=-3x+4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\\\x+\dfrac{1}{3}y=\dfrac{4}{3}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Substituting the value of y from equation (i) in equation (ii), we get

$x+\dfrac{1}{3}(-3x+4)=\dfrac{4}{3}\\\\\\\Rightarrow x-x+\dfrac{4}{3}=\dfrac{4}{3}\\\\\\\Rightarrow \dfrac{4}{3}=\dfrac{4}{3},$

which is always true.

So, the given system of equations will have an infinite number of solutions.

Let x = k, then from equation (i), we get

$y=-3k+4.$

Thus, all the solutions of the given system are

(x, y) = (k, -3k + 4), where k is any real number.