MathMatters 3: An Integrated Program, Reteaching Workbook by McGraw-Hill Education

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E x a m p l e Solve. 4x Ϫ 3y ϭ 11 2x ϭ 4y ϩ 3 Solution Write each equation in standard form. 4x Ϫ 3y ϭ 11 2x ϭ 4y ϩ 3 ➝ 2x Ϫ 4y ϭ 3 Multiply to obtain an equivalent system of equations in which the coefficients of one of the variables are either the same or the opposite. Then add or subtract. 4x Ϫ 3y ϭ 11 ➝ 4x Ϫ 3y ϭ 11 ➝ 4x Ϫ 3y ϭ 11 2x Ϫ 4y ϭ 3 ➝ Ϫ2(2x Ϫ 4y) ϭ 3(Ϫ2) ➝ Ϫ4x ϩ 8y ϭ Ϫ6 5y ϭ 5, so y ϭ 1 Choose one of the original equations, for example 4x Ϫ 3y ϭ 11. Substitute 1 for y. 4x Ϫ 3(1) ϭ 11 4x Ϫ 3 ϭ 11 4x ϭ 14 1 x ϭ 3ᎏ2ᎏ The solution is 3ᎏ1 2ᎏ, 1 .

Glencoe/McGraw-Hill 55 MathMatters 3 Name _________________________________________________________ RETEACHING Date ____________________________ 7-6 PARALLEL LINES AND PROPORTIONAL SEGMENTS Properties of similar triangles can be used to determine whether lines are parallel and to show proportions. • A line parallel to one side of a triangle that intersects each of the other two sides at a point other than the vertex divides the sides proportionately. • A segment that joins the midpoints of two sides of a triangle is parallel to the third side.

A line parallel to one side of a triangle that intersects each of the other two sides at a point other than the vertex divides the sides proportionately. • A segment that joins the midpoints of two sides of a triangle is parallel to the third side. E x a m p l e Find the value of x ෆ || A ෆB ෆ. given ෆ DE Solution Since ෆ DE ෆ || A ෆB ෆ, and D ෆE ෆ intersects ෆ AC ෆ and B ෆC ෆ at a point other ෆ divides the sides proportionately. than the vertex, ෆ DE To find x, write and solve a proportion. AD BE → ϭ 10 ᎏ ᎏϭᎏ ᎏ5 CD Cᎏ E xᎏ ᎏ6ᎏ 30 ϭ 10x 3ϭx So x is 3.

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