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6. 1 Equations in Two Variables Academic Objective We will find solutions to equations with two variables. Language Objective I can find ordered pairs (points) that make an equation true. Assignment Workbook Page 79 #1 -15 Tables on 1 -3 & 10 -15 need 4 ordered pairs.

Point ~ a location of a dot determined by an ordered pair. Coordinate Plane Ordered Pair ~ create a point on the coordinate plane. (x, y) With two points you can create a line. (2, 1) (4, 2) Equations with two variables (x, y) are used to find points that create lines.

Finding solutions or coordinates! 4 x + y = 15 x Equation y (x, y) -1 4( -1 ) + y = 15 19 (-1, 19) 0 4( 0 ) + y = 15 15 (0, 15) 1 4( 1 ) + y = 15 11 (1, 11) 2 4( 2 ) + y = 15 7 (2, 7)

Finding solutions or coordinates! x Equation y (x, y) -2 -2 2 (-2, 2) 0 0 3 (0, 3) 2 2 4 (2, 4) 4 4 5 (4, 5)

Plug In and Check Tell whether the ordered pair is a solution of the equation. X + 3 y = 14; (7, -6) ( ) + 3( ) = 14 Set up with ( ) ( 7 ) + 3( -6 ) = 14 Substitute 7 + (-18) = 14 ? ? ? -11 14, so no it is not a solution!

Plug In and Check Tell whether the ordered pair is a solution of the equation. 4 X - 2 y = -28; (-5; 4) 4( ) - 2( ) = -28 Set up with ( ) 4( -5) - 2( 4 ) = -28 Substitute -20 - 8 = -28 ? ? ? -28 = -28, so it is a solution!