Verify that the points of intersection specified on the graph of each nonlinear system are solutions of the system by substituting directly into both equations.

y = 3x²

x² + y² = 10

Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components.

x² - y = 0

x + y = 2

Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components.

y = x² - 2x + 1

x - 3y = -1

Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components.

2xy + 1 = 0

x + 16y = 2

Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components.

3x² - y² = 11

xy = 12

Solve each problem using a system of equations in two variables. See Example 6. Find two numbers whose sum is 17 and whose product is 42.

Solve each problem using a system of equations in two variables. See Example 6. Find two numbers whose squares have a sum of 100 and a difference of 28.

Solve each problem using a system of equations in two variables. See Example 6. Find two numbers whose ratio is 9 to 2 and whose product is 162.

Solve each problem using a system of equations in two variables. See Example 6. The longest side of a right triangle is 13 m in length. One of the other sides is 7 m longer than the shortest side. Find the lengths of the two shorter sides of the triangle.

Answer each question. Does the straight line 3x - 2y = 9 intersect the circle x² + y² = 25? (Hint: To find out, solve the system formed by these two equations.)

Answer each question. A line passes through the points of intersection of the graphs of y = x² and x² + y² = 90. What is the equation of this line?

Consider the following nonlinear system. Work Exercises 75 –80 in order.

y = | x - 1 |

y = x² - 4

How is the graph of y = | x - 1 | obtained by transforming the graph of y = | x |?

Consider the following nonlinear system. Work Exercises 75 –80 in order.

y = | x - 1 |

y = x² - 4

Use the definition of absolute value to write y = | x - 1 | as a piecewise-defined function.

Match each system of inequalities with the correct graph from choices A–D. x ≥ 5 y ≤ -3

Graph each inequality. x + 2y ≤ 6

Graph each inequality. x ≤ 3

Graph each inequality. y < 3x² + 2

Graph each inequality. y > (x - 1)² + 2

Graph each inequality. x² + (y + 3)² ≤ 16

Graph each inequality. y > 2^x + 1

Graph each inequality. y ≤ log(x - 1) - 2

Match each inequality with the appropriate calculator graph in A–D. Do not use a calculator y ≤ -3x - 6

Graph the solution set of each system of inequalities.

x + y ≥ 0

2x - y ≥ 3

Graph the solution set of each system of inequalities.

2x + y > 2

x - 3y < 6

Graph the solution set of each system of inequalities.

3x + 5y ≤ 15

x² + y² < 9

Graph the solution set of each system of inequalities.

4x - 3y ≤ 12

y ≤ x²

Graph the solution set of each system of inequalities.

y ≥ (x - 2)² + 3

y ≤ -(x - 1)² + 6

Graph the solution set of each system of inequalities.

y ≥ x² + 4x + 4

y < -x²

Graph the solution set of each system of inequalities.

$3x-2y\ge 6$

$x+y\le -5$

$y\le 4$

Graph the solution set of each system of inequalities.

$x\le 4$

$x\ge 0$

$y\ge 0$

$x+2y\ge 2$