Solve the linear equation for one variable. In this example, the top equation is linear. If you solve for x, you get x = 3 + 4y. Substitute the value of the variable into the nonlinear equation. When you plug 3 + 4y into the second equation for x, you get (3 + 4y)y = 6. Solve the nonlinear equation for the variable. When you distribute the y, you get 4y2 + 3y = 6. Because this equation is quadratic, you must get 0 on one side, so subtract the 6 from both sides to get 4y2 + 3y – 6 = 0. You have to use the quadratic formula to solve this equation for y:  Substitute the solution(s) into either equation to solve for the other variable. Because you found two solutions for y, you have to substitute them both to get two different coordinate pairs. Here’s what happens when you do:  Therefore, you get the solutions to the system:  These solutions represent the intersection of the line x – 4y = 3 and the rational function xy = 6.
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Solve the linear equation for one variable. In this example, the top equation is linear. If you solve for x, you get x = 3 + 4y. Substitute the value of the variable into the nonlinear equation. When you plug 3 + 4y into the second equation for x, you get (3 + 4y)y = 6. Solve the nonlinear equation for the variable. When you distribute the y, you get 4y2 + 3y = 6. Because this equation is quadratic, you must get 0 on one side, so subtract the 6 from both sides to get 4y2 + 3y – 6 = 0. You have to use the quadratic formula to solve this equation for y:  Substitute the solution(s) into either equation to solve for the other variable. Because you found two solutions for y, you have to substitute them both to get two different coordinate pairs. Here’s what happens when you do:  Therefore, you get the solutions to the system:  These solutions represent the intersection of the line x – 4y = 3 and the rational function xy = 6.