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### 21 Cards in this Set

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 Is the linear equation 3x +4y =23 equivalent if x=5 and y=2? Yes the answer is 23 on both sides of the equation. What is a linear equation with two variables? An equation that may be written in the form ax + by =c, where the numbers a, b, and c are all real numbers such that a and b are not both, 0. What are coordinates? The numbers x and y written in the form (x, y). What is a dependent variable? The second element of an ordered pair, usually y. What is an independent variable? The first element of an ordered pair, usually x. What is a number plane? All points in the plane determined by the intersecting, perpendicular x axis (horizontal axis) and y axis (vertical axis). What is an origin? The zero point where the x and y axes intersect in the number plane. What is a quadrant? Each of the four regions of the number plane formed by the intersection of the x and y axes. Define Rectangular coordinate system? The number plane formed by the intersection of the x and y axes. Also called the Cartesian coordinate system. Define ordered pair? Numbers in the form (x, y) that correspond to points in the number plane; also used to write solutions of systems of equations with two variables. Define x axis? The horizontal axis in the number plane. Define y axis? The vertical axis in the number plane. Define x intercept? The x coordinate of the point where the graph crosses the x axis. Define y intercept? The y coordinate of the point where the graph crosses the y axis. Complete the three ordered pair solutions of this equation: x + y = 5 and your ordered pairs are (3, ) (8, ) (-2, ) x + y = 5 3 + y = 5 3 + y - 3 = 5 - 3 = 2 The first ordered pair is (3, 2). x + y = 5 8 + y = 5 8 + y - 8 = 5 - 8 = -3 The second ordered pair is (8, -3) x + y = 5 -2 + y = 5 -2 + y +2 = 5 + 2 = 7 The third ordered pair is (-2, 7) Complete the three ordered pair 6x - y = 0 Ordered pairs are (3, ) (5, ) (-2, ) 6x - y = 0 6(3) - y = 0 18 - y = 0 18 - y + 18 = 0 + 18 = 18 First ordered pair (3, 18) 6x - y = 0 6(5) - y = 0 30 - y = 0 30 - 30 - y = 0 - 30 = -30 -y = -30 -y/-1 = -30/-1 = 30 Second ordered pair is (5, 30) 6x - y = 0 6(-2) - y = 0 -12 - y = 0 -12 + 12 - y = 0 + 12 = 12 -y = 12 -y/-1 = 12/-1= -12 Third ordered pair is (-2, -12) Complete the three ordered pair solution 9x - 2y = 5 Ordered pairs are (1, ) (0, ) (-3) 9x - 2y = 5 9x - 2y - 9x = 5 - 9x -2y = 5 - 9x -2y / -2 = 5 - 9x / -2 y = 5 - 9x /-2 y = 5 - 9(1) /-2 y = 5 - 9 / -2 = 2 First ordered pair is (1, 2) y = 5 - 9(0) / -2 y = 5 - 0 / -2 y = 5 / -2 Second ordered pair is (0, -5/2) y = 5 - 9(-3) / -2 y = 5 + 27 / -2 y = 32 / -2 y = -16 The third ordered pair is (-3, -16) Complete the three ordered pair solution: x + 2y = 8 Ordered pairs are (3, ) (0, ) (-4, ) x + 2y = 8 3 + 2y = 8 3 -3 + 2y = 8 - 3 =5 2y = 5 2y/2 = 5/2 y=5/2 or 2 1/2 First ordered pair is (3, 0) x + 2y =8 0 + 2y =8 0 - 0 + 2y = 8 - 0 =0 2y = 8 2y/2 = 8/2=4 y = 4 Second ordered pair is (0, 4) x + 2y =8 -4 + 2y = 8 -4 + 4 + 2y = 8 + 4 2y = 12 2y/2 =12/2 =6 y = 6 Third ordered pair is (-4, 6) Complete the three ordered pair solution: 2x - 3y =12 Ordered pairs are (3, ) (0, ) (-3, ) 2x - 3y =12 2(3) - 3y =12 6 - 3y =12 6 - 6 -3y = 12 - 6 =6 -3y = 6 -3y/-3 = 6/-3 y = -2 First ordered pair is (3, -2) 2x - 3y = 12 2(0) - 3y =12 -3y = 12 -3y/-3 = 12/-3 y = -4 Second ordered pair is (0, -4) 2x - 3y = 12 2(-3) - 3y =12 -6 + 6 - 3y =12 + 6 =18 -3y = 18 -3y/-3 = 18/-3= -6 Third ordered pair is (-3, -6) Solve for y in this problem: 6x + y = 15 y = -6x + 15 Complete the three ordered pair with the given equation: 3x - 4y = 24 Ordered pairs are (-4, ) (0, ) (4, ) 3x - 4y=24 3(-4) - 4y =24 -12 + 12 - 4y =24 + 12 =36 -4y = 36 -4y/-4 = 36/-4 y = -9 First ordered pair is (-4, -9) 3x - 4y = 24 3(0) - 4y - 24 -4y = 24 -4y/-4 = 24/-4 y = -6 Second ordered pair is (0, -6) 3x - 4y = 24 3(4) - 4y = 24 12 - 12 - 4y = 24 - 12 = 12 -4y = 12 -4y/-4 = 12/-4 y = -3 Third ordered pair is (4, -3)