Question

Rewrite the equation so that x is a function of y. Then use the result to find x when y = -2, -1, 0, and 1. $$3 x+y=7$$

Short answer

The solutions for x when y = -2, -1, 0, and 1 are respectively 3, \(\frac{8}{3}\), \(\frac{7}{3}\), and 2.

Step-by-step solution

Rearrange the Equation

Currently, the equation is in the standard form \(3x + y = 7\). To isolate \(x\), subtract \(y\) from both sides, then divide by 3. This gives the equation in terms of \(x\), \(x = \frac{7 - y}{3}\).

Find x for y = -2

Substitute \(y = -2\) into the equation \(x = \frac{7 - y}{3}\), then calculate to find \(x\). This yields \(x = \frac{7 - (-2)}{3} = 3\).

Find x for y = -1

Substitute \(y = -1\) into the equation \(x = \frac{7 - y}{3}\), then calculate to find \(x\). This yields \(x = \frac{7 - (-1)}{3} = \frac{8}{3}\).

Find x for y = 0

Substitute \(y = 0\) into the equation \(x = \frac{7 - y}{3}\), then calculate to find \(x\). This yields \(x = \frac{7 - 0}{3} = \frac{7}{3}\).

Find x for y = 1

Substitute \(y = 1\) into the equation \(x = \frac{7 - y}{3}\), then calculate to find \(x\). This yields \(x = \frac{7 - 1}{3} = 2\).