Write the two equations in ax + by = c form. For instance, you might have two lines with the following initial equations: 3y = -2x + 4 and -5y = -6x + 8. Change the positive or negative value of any terms that you move across the equals sign, so that in this example, you would change the equations to:
2x + 3y = 4 and 6x - 5y = 8
Draw two brackets in which you write the x and y coefficients of the first equation in the top horizontal row and the x and y coefficients of the second equation in the second horizontal row. In this example, you would have the 2 and the 3 on the top row and the 6 and -5 in the second row within the set of brackets.
Draw a set of parentheses to the right of the bracket that you drew in step two. Write "x" on top and "y" underneath within these parentheses.
Draw another set of parentheses to the right of the set that you drew in step three, and separate the two sets of parentheses with an equal sign in between. In the second set of parentheses, write the constant (the number without a variable) from the first equation on top and the constant from the second equation underneath. In this example, you would write 4 on top and 8 underneath within this set of parentheses.
Correlate an "a" and a "b" with the 2 and 3 in the top of the bracket and a "c" with the 4 in the second set of parentheses. Correlate a "d" and an "e" with the 6 and -5 in the bottom row of the bracket and an "f" with the 8 in the bottom part of the second set of parentheses.
Multiply c times e. In this equation you would multiply 4 x -5 to get -20.
Multiply b times f. In this equation you would multiply 3 x 8 to get 24.
Subtract your answer from step seven from your answer from step six. Therefore, you would subtract 24 from -20 to get -44.
Multiply a times d. In this example you would multiply 2 x -5 to get -10.
Multiply b times c. Therefore, you would multiply 3 x 6 to get 18.
Subtract your answer from step 10 from your answer from step nine. In this example, you would subtract 18 from -10 to get -28.
Write a fraction with your answer from step eight in the numerator (on top) and your answer from step 11 in the denominator (on bottom). For this problem, you would write -44/-28. Simplify the fraction if possible. This fraction simplifies to 11/7. This fraction is the solution for "x" for both equations. Therefore, x = 11/7.
Multiply a times f and d times c. For this example you would multiply 2 x 8 and 6 x 4. The first answer is 16 and the second answer is 24.
Subtract the second answer from step 13 from the first. Therefore, you would subtract 24 from 16 to get -8.
Multiply a times e and b times d. In this example you would multiply 2 x -5 and 3 x 6. The first answer is -10, and the second answer is 18.
Subtract the second answer from step 15 from the first. Therefore, you would subtract 18 from -10 to get -28.
Write your answer from step 14 in the numerator and your answer from step 16 in the denominator to solve for y. In this example, you would write -8/-28, which is simplified to 2/7. Therefore, y = 2/7.