By Benjamin Braley Updated Aug 30, 2022
Algebra 1 can feel intimidating—especially when you’re asked to solve for one or two unknowns at once. This concise guide walks you through each step, from the order of operations to the elimination method, so you can tackle any single‑ or multi‑variable equation with confidence.
Determine whether the problem involves one variable (usually x or y) or multiple variables. Knowing the scope of the equation sets the stage for the rest of the process.
Start inside parentheses, then simplify exponents (e.g., square roots, x²). After that, perform multiplication and division, followed by addition and subtraction. Writing each step beneath the previous one keeps your work organized.
For single‑variable problems, you’ll work with that lone symbol. For two‑variable problems, you’ll be given two equations, each containing the same pair of variables such as x and y.
Rewrite the equations so that the chosen variable appears in the same position on both lines. Multiply one equation so the coefficients of that variable match (e.g., make both coefficients 4). Subtract one equation from the other, being careful with signs, to eliminate that variable and leave a single‑variable equation.
Move any standalone numbers to the opposite side of the equals sign, then divide both sides by the coefficient in front of the variable. This step solves for one of the unknowns.
Insert the value you just found into the other equation, replacing every instance of the solved variable. This reduces the remaining equation to a single unknown.
Repeat the process of moving numbers and dividing by the coefficient to isolate and solve the last variable.
Plug both values back into the original equations to confirm they satisfy both conditions. A quick check ensures no arithmetic errors slipped through.
