By Nicole Harms | Updated Aug 30, 2022

When faced with a system of linear equations, the most reliable approach is to solve algebraically. This method removes the possibility of graphing errors and eliminates the need for graph paper, making it ideal for systems involving fractions or complex solutions.

Step 1

Choose the equation that is easiest to isolate a variable. For the system

2x – 3y = –2
4x + y = 24

the second equation can be solved for y by subtracting 4x from both sides:

y = –4x + 24

Step 2

Substitute this expression for y into the first equation:

2x – 3(–4x + 24) = –2

Step 3

Expand and simplify:

2x + 12x – 72 = –2 → 14x – 72 = –2

Step 4

Isolate x:

14x = 70 → x = 5

Step 5

Insert x = 5 into one of the original equations, e.g., 4x + y = 24:

4(5) + y = 24

Step 6

Solve for y:

20 + y = 24 → y = 4

Step 7

State the solution as an ordered pair:

(5, 4)

Step 8

Verify by plugging (5, 4) back into both equations. Both yield true statements, confirming the solution.

TL;DR (Too Long; Didn't Read)

Select the simplest equation to isolate a variable. Substitute its value into the other equation, solve for the remaining variable, and verify the result. This substitution method is a straightforward, error‑free way to solve linear systems.

Warning

Always double‑check your answer to catch any arithmetic slip‑ups.