Q. Solve this system of equations: \(y = x – 4\) and \(y = 6x – 10\).

Solution — step-by-step

1. We are given two expressions for y. Because both right-hand sides equal y, they are equal to each other. Set them equal:

   \[ x – 4 = 6x – 10 \]

   Explanation: If y = A and y = B, then A = B. This reduces the system to a single equation in x.

2. Eliminate x from one side by subtracting x from both sides:

   \[ x – 4 – x = 6x – 10 – x \]

   Simplify each side:

   \[ -4 = 5x – 10 \]

   Explanation: Subtracting the same quantity from both sides preserves equality. The left side becomes -4 because x – x = 0; the right side combines 6x – x = 5x.

3. Isolate the term with x by adding 10 to both sides:

   \[ -4 + 10 = 5x – 10 + 10 \]

   Simplify:

   \[ 6 = 5x \]

   Explanation: Adding 10 to both sides cancels the -10 on the right, leaving 5x alone on the right-hand side.

4. Divide both sides by 5 to solve for x:

   \[ x = \frac{6}{5} \]

   Explanation: Division by 5 isolates x because 5x divided by 5 equals x.

5. Find y by substituting x back into either original equation. Using y = x – 4:

   \[ y = \frac{6}{5} – 4 \]

   Write 4 as a fraction with denominator 5: 4 = \frac{20}{5}, then

   \[ y = \frac{6}{5} – \frac{20}{5} = -\frac{14}{5} \]

   Explanation: Substitution gives the corresponding y-value. Converting to common denominators yields the exact fraction.

6. Optional check: Use the second equation y = 6x – 10 to verify the same y:

   \[ y = 6\left(\frac{6}{5}\right) – 10 = \frac{36}{5} – \frac{50}{5} = -\frac{14}{5} \]

   Both equations give the same y, so the solution is consistent.

7. Final answer (ordered pair):

   \[ \left(\frac{6}{5}, -\frac{14}{5}\right) \]