We will solve this and similar problems involving two or three equations and two or three variables in this section. Understanding the correct approach to setting up problems such as these one makes finding a solution a matter of following a pattern. How much did John invest in each type of fund? He earned $670 in interest the first year.
John invested $4,000 more in municipal funds than in municipal bonds. John received an inheritance of $12,000 that he divided into three parts and invested in three ways: in a money-market fund paying 3% annual interest in municipal bonds paying 4% annual interest and in mutual funds paying 7% annual interest. How can the company determine if it is making a profit with its new line? How many skateboards must be produced and sold before a profit is possible?Â
The manufacturer tracks its costs, which is the amount it spends to produce the boards, and its revenue, which is the amount it earns through sales of its boards. There are three possible types of solutions for a system of nonlinear equations involving a parabola and a line.A skateboard manufacturer introduces a new line of boards.
There is, however, a variation in the possible outcomes. We solve one equation for one variable and then substitute the result into the second equation to solve for another variable, and so on. The substitution method we used for linear systems is the same method we will use for nonlinear systems. Any equation that cannot be written in this form in nonlinear. Recall that a linear equation can take the form Ax+By+C=0. Solve a system that represents the intersection of a circle and an ellipse using elimination.Ī system of nonlinear equations is a system of two or more equations in two or more variables containing at least one equation that is not linear.Solve a system that represents the intersection of a circle and a line using substitution.Solve a system that represents the intersection of a parabola and a line using substitution.
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