Solve Two Equations at Once (Simultaneous Equations), Step by Step

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Opens on Chapter 14’s example: the posters: 40 posters, large at $15 and small at $8, $446 in all.

a·x + b·y = c

d·x + e·y = f

First letter

Second letter

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Enter your numbers, then press Work it out.

How it works

Substitution: when a letter has nothing in front of it, make it the subject of its equation (y = 40 − x) and put that in place of the letter in the other equation, which then has one letter and solves as usual. Elimination: multiply one or both equations so a letter has the same number in front in both, then take one equation from the other (or add them, if the signs differ) so that letter cancels. Either way, put the first answer back to find the second, and check both in both equations. On the graph each equation is a line and the answer is where they cross; parallel lines mean no answer, and the same line means every point on it works.

From the book, Chapter 14. The posters: 18 large and 22 small. y = 2x + 1 and y = −x + 7 cross at (2, 5). Mulch is $7 a bag and gravel $9. The blend takes 20 lb of the $8 coffee and 10 lb of the $14. The play sold 80 adult and 70 child tickets. Every chapter and its calculator →

Numbers can be typed as 1,450, $38, 0.40, 12%, 1/6 or 2 3/8. The algebra is done with exact fractions, so 1/3 stays 1/3; decimals are rounded half up, the way the book rounds. Everything stays in your browser: no sign-up, nothing stored or sent.