写出每条直线的方程，y{\displaystyle y}在等式左侧。 让两个等式右侧相等。 求x 用这个x{\displaystyle x}-值来求解y{\displaystyle y}。 检查计算结果。 写出交点的x{\displaystyle x}和y{\displaystyle y}坐标。 处理异常结果。

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If necessary, rearrange the equation so y{\displaystyle y} is alone on one side of the equal sign. If the equation uses f(x){\displaystyle f(x)} or g(x){\displaystyle g(x)} instead of y{\displaystyle y}, separate this term instead. Remember, you can cancel out terms by performing the same action to both sides.  If you do not know the equations, find them based on the information you have.  Example: Your two lines are y=x+3{\displaystyle y=x+3} and y−12=−2x{\displaystyle y-12=-2x}. To get y{\displaystyle y} alone in the second equation, add 12 to each side: y=12−2x{\displaystyle y=12-2x} We're looking for a point where the two lines have the same x{\displaystyle x} and y{\displaystyle y} values; this is where the lines cross. Both equations have just y{\displaystyle y} on the left side, so we know the right sides are equal to each other. Write a new equation that represents this.  Example: We know y=x+3{\displaystyle y=x+3} and y=12−2x{\displaystyle y=12-2x}, therefore x+3=12−2x{\displaystyle x+3=12-2x}. . The new equation only has one variable, x{\displaystyle x}. Solve this using algebra, by performing the same operation on both sides. Get the x{\displaystyle x} terms on one side of the equation, then put it in the form x=??{\displaystyle x=??}. (If this is impossible, skip down to the end of this section.)   Example: x+3=12−2x{\displaystyle x+3=12-2x}  Add 2x{\displaystyle 2x} to each side: 3x+3=12{\displaystyle 3x+3=12} Subtract 3 from each side: 3x=9{\displaystyle 3x=9} Divide each side by 3:  x=3{\displaystyle x=3}. Choose the equation for either line. Replace every x{\displaystyle x} in the equation with the answer you found. Do the arithmetic to solve for y{\displaystyle y}.   Example: x=3{\displaystyle x=3} and y=x+3{\displaystyle y=x+3}  y=3+3{\displaystyle y=3+3} y=6{\displaystyle y=6} It's a good idea to plug your x{\displaystyle x}-value into the other equation and see if you get the same result. If you get a different solution for y{\displaystyle y}, go back and check your work for mistakes.  ...