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1c. The equation 3x2 + y = 9 is not a linear equation since the exponent of x is 2. 1d. The equation is a linear equation because the exponents of the variables are both 1. It is, however, not written in standard form. To write it in standard form, we need to clear fractions and get the variable terms on one side of the equation and the constant on the other. y = 3 2 x - 2 2( y) = 2a3 2 x - 2b Multiply each side by the LCD, 2. 2y = 3x -4 Apply the distributive property and simplify. 2y - 3x = 3x - 4 - 3x Subtract 3x from each side. -3x + 2y=-4 Rewrite the equation with the x-term fi rst. -1(-3x + 2y) = -1(-4) Multiply each side by -1. 3x - 2y =4 Simplify. So, A = 3, B = -2, and C = 4. Student Check 1 Determine if the equation is a linear equation in two variables. If the equation is a linear equation in two variables, write it in standard form and identify the values of A, B, and C. a. x - 2y = -4 b. x = 4 c. x2 + y2 = 25 d. y = 2 3 x + 4 Graphing Linear Equations in Two Variables In Section 3.1, we learned how to graph equations in two variables. In this section, we will specifically discuss how to graph linear equations in two variables. Consider the equation x + y = 5. The solutions of this equation are ordered pairs (x, y) such that the sum of the x-coordinate and y-coordinate is 5. There are many ordered pairs that satisfy this condition. Some of the solutions are listed next. x y (x, y) 5 0 (5, 0) 4 1 (4, 1) 3 2 (3, 2) 2 3 (2, 3) 1 4 (1, 4) 0 5 (0, 5) -1 6 (-1, 6) -2.5 7.5 (-2.5, 7.5) This list of solutions continues indefi nitely. Since we cannot possibly list all of the solutions of this equation, we plot the points and try to recognize a pattern that enables us to connect the points and extend the graph. Notice that the graph of this equation is a line. This is the reason the equation is called a linear equation. Any point on the graph of this line is a solution of the equation x + y = 5. Note that we put arrows on the ends of the graph to indicate there are infinitely many solutions. Objective 2 ▶ Plot points to graph a linear equation in two variables. 5 + 0 = 5 4 + 1 = 5 3 + 2 = 5 2 + 3 = 5 1 + 4 = 5 0 + 5 = 5 -1 + 6 = 5 -2.5 + 7.5 = 5 8 y (–1, 6) (0, 5) 2 (1, 4) (2, 3) (4, 1) 2 4 (5, 0) (3, 2) (–2.5, 7.5) –4 –2 x 210 Chapter 3 Linear Equations in Two Variables


hendricks_beginning_algebra_1e_ch1_3
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