D3notes - Supplementary Course Module D Solving Equations...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Supplementary Course Module D: Solving Equations and Inequalities Assignment 3 & Systems of Equations; Inequalities Solving Systems of Equations & To solve a system of two equations in two variables, say x and y , we are looking for all pairs of values ( x; y ) which simultaneously satisfy both equations. & There are two common methods which are used for such problems: elimination and substitution. example: Solve the system 2 x ¡ 3 y = 1 1 8 y ¡ 6 x = 4 2 Substitution: From 1 : x = 1 2 (1 + 3 y ) Sub into 2 : ¡ 6 & 1 2 (1 + 3 y ) ¡ + 8 y = 4 y = ¡ 7 Sub y = ¡ 7 into 1 : x = 1 2 (1 ¡ 21) = ¡ 10 ) there is one solution: ( ¡ 10 ; ¡ 7) Elimination: 1 ¢ 3 6 x ¡ 9 y = 3 2 ¡ 6 x + 8 y = 4 Add: ¡ y = 7 y = ¡ 7 & Sub y = ¡ 7 into 1 : 2 x + 21 = 1 2 x = ¡ 20 x = ¡ 10 ) there is one solution: ( ¡ 10 ; ¡ 7) example: Solve the system 3 x ¡ 4 y = 8 1 ¡ 6 x + 8 y = ¡ 16 2 1 ¢ 2 6 x ¡ 8 y = 16 2 ¡ 6 x + 8 y = ¡ 16 Add: y = 0 y 2 R ) there are in&nite solutions (such a system is called dependent). example: Solve the system 6 x ¡ 8 y = 16 1 ¡ 6 x + 8 y = 16 2 Add: y = 32- > no solution exists ) the system has no solution (such a system is called inconsistent). & A system of equations involving three unknowns may also be solved if three equations linking the variables are given. (And a system of equations involving four unknowns may be solved if 4 equations are known, etc.) & such systems may require various applications of both the substitution and elimination methods example: Solve the system 2 x + y + z = 7 1 x ¡ y + 2 z = 11 2 5 x + y ¡ 2 z = 1 3 Add 2 + 3 : 6 x = 12 () x = 2 Sub into...
View Full Document

{[ snackBarMessage ]}

Page1 / 4

D3notes - Supplementary Course Module D Solving Equations...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online