X 4y 3 0x 2y 0
[DOC File]SIMULTANEOUS EQUATIONS
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For the line 3x + 2y = 8 . x 0 2 4 y 4 1 -2 For the line x – 4y = -2. x 2 6 10 y 1 2 3 Exercise: Draw the two lines on the same pair of axes and find the point of intersection. State the x and y co-ordinates as the solution. Example 5. Solve the simultaneous equations below graphically. x + y = 3. y – x2 = 1.
[DOC File]Chapter 2
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x = 3 x = 3, y = 1, z = 2. 10. x + 2y = 3. y + z = 3. x + 3z = 2. x + 2y = 3 multiply second equation by 2. 2y + 2z = 6 subtract from first. x - 2z = -3. Use this equation with the third. x - 2z = -3. x + 3z = 2 subtract - 5z = -5. z = 1. x + 3(1) = 2. x = -1. y + 1 = 3. y = 2 (-1, 2, 1) 11.
[DOC File]Revision Exercises
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2y = 16. y = 8 (vi) 2x+2y-5z = -5. x-y+z = 3-3x+y+2z = -2. STEP 1: Express in terms of same value of one variable (2x) Equation 1: 2x+2y-5z = -5. 2x = -5-2y+5z. Equation 2: (x-y+z = 3) multiplied by 2. 2x-2y+2z = 6. 2x = 6+2y-2z. STEP 2: Substitute value of eq1 for eq2-5-2y+5z = 6+2y-2z. STEP 3: Collect the terms-2y+5z-2y+2z = 6+5-4y+7z = 11
[DOC File]Algebra Review
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ALGEBRA REVIEW. Add as indicated: 1. (2ac) +(–6ac) +(9ac) = 5ac. 2. 3x +(–7x) = –4x . 3. (–8a) –(–3a) –(2a) = –7a . 4. (5x) –(6x) –(7x) = –8x
[DOC File]Solving System of Equations by Graphing (using x and y ...
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3. 3x + 4y = -2-2x – 2y = 0. Solve by elimination _____ Solve by Substitution (solve for either y or x and insert it into the other equation) Solve by graphing (show work – get the 2 points) _____ 4. 2x + 3y = -10. X + 4y = -10. Solve by elimination ...
[DOC File]Suggested Answer Key
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Problems 4.2, 4.4, 4.6, 4.7 and 4.9. 4.2 a. A young connoisseur has $300 to spend to build a small wine cellar. She enjoys two vintages in particular: an expensive 1987 French Bordeaux (WF) and $20 per bottle and a less expensive 1993 California varietal wine (WC) priced at $4.
[DOC File]Sketching the Solution Set of a Linear Inequality
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Substituting x=0, y=0 in the inequality gives . 3(0) - 4(0) ≤ 12. Since this is a true statement, (0, 0) is in the solution set, so the solution set consists of all points on the same side as (0, 0). This region is left unshaded, while the (grey) shaded region is blocked out. Graphing Lines: Take for example the line 2 x – 3 y – 6 = 0.
[DOC File]CHAPITRE V - e-monsite
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Le plan est muni d’un repère orthonormé (O, I, J), on considère les droites (L) et (L’) d’équation respectives x – 2y – 3 = 0 et y = - 2x + 1 mettre l’équation de (L) sous la forme y = ax + b où a et b sont des nombres réels.
[DOC File]lee
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(Sol.) L[y”+2xy’-4y]=L(1)= , , , ∴ c=0 y”+9y=cos(2t), y(0)=1 and y(π/2)=-1 (Sol.) y(t)= (x-1)y”-xy’+y=0, y(0)=y’(0)=1 (台大機研) y”+2ty’-4y=1, y(0)=y’(0)=0 (2002台科大電研)
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