Question

Use substitution to solve the system of linear equations. In your final answer, include all of your work.

{ y = -3x + 4
{ x + 1/3 y = 4/3




WRITER

Answer 1

We are given
y = −3x + 4
x + (1/3)y = 4/3.

Substitute y = −3x + 4 into the second equation:
x + (1/3)(−3x + 4) = 4/3
x + (1/3)(−3x) + (1/3)(4) = 4/3
x − x + 4/3 = 4/3
4/3 = 4/3.

This identity holds for every x, so the two equations are dependent (the same line). Therefore there are infinitely many solutions: all points (x,y) with y = −3x + 4.

Parametrically: (x,y) = (t, −3t + 4) for any real number t. (For example, t = 0 gives (0,4), t = 1 gives (1,1), etc.)