I have to use matrices to answer this problem, no elimination nor substitution. 4x - 5y = 13 2x - 7y = 24 a=4 b= -5 c= 2 d= -7 e=13 f=24 d= |a b| d=|4 -5| d= -28 + 10 d= -18 ----|c d|------|2 -7| x=|e b| x=|13 -5| x= -91 +120 x= -29/18 ---|f d|------|24 -7| y=|a e| y=|4 24| y= 96 - 26 y= -80/18 ---|c f|-------|2 13| (-29/18, -80,18) GAAAAH I DUNNO WHERE I WENT WRONG!!!

4x-5y=13 2x-7y=24 4x-5y=13 4x-13=5y ((4x-13)/5)=y 2x-7((4x-13)/5)=24 I'll take you this far... math bores me bro, sorry LOL

Using matrices: 4x - 5y = 13 2x - 7y = 24 (4 -5)(x) = (13) (2 -7)(y) = (24) (a b) (c d) goes to (d -b) (-c a) divided by (ad-bc) So (x) = (-7 5) (13) divided by -18 (y) = (-2 4) (24) divided by -18 x = -7*13+5*24 divided by -18 y = -2*13+4*24 divided by -18 x=-29/18 y=-70/18 Sorry, the formatting has messed up your answer and I can't see where you went wrong. No wait I see it you have 96-26 = 80 :)

[^^^] = [ 4x - 5y = 13 ], [ 2x - 7y = 24 ] = [ 4x - 5y = 13 ], [ { 2x - 7y } X 2 = 24 X 2 ] = [ 4x - 5y = 13 ], [ 4x - 14y = 48 ] = [ 4x = 13 + 5y], [ 4x = 48 + 14y ] [^^^] = [ 4x = 13 + 5y = 48 + 14y ] = [ 13 + 5y = 48 + 14y ] = [ 5y - 14y = 48 - 13 ] = [ (+5y) - (+14y) = (+48) - (+13) ] = [ (+5y) + (-14y) = (+48) - (+13) ] = [ (-14y) + (+5y) = (+48) - (+13) ] = [ (-14y) - (-5y) = (+48) - (+13) ] = [ (-9y) = (+35) ] = [ (-9)y = (+35) ] = [ y = (+35)/(-9) ] = [ y = { -< 35/9 > } ] = [ y = { -< ( 35 X 2 )/( 9 X 2) > } ] = [ y = { -< ( 70 )/( 18 ) > } ] = [ y = { -< 70/18 > } ] [^^^] = [ 2x - 7y = 24 ] = [ 2x - 7{ -< 35/9> } = 24 ] = [ 2x = 24 - 7{ -< 35/9> } ] = [ x = [ 24 - 7{ -< 35/9> } ] / 2 ] = [ x = { -< 29/18 > } ]

well, i suggest that you use elimination. man it's darn easier. 4x - 5y = 13 2x - 7y = 24 multiply equation 2 by 2 and then subtract it from the first equation to eliminate x, giving you 4x-5y=13 -4x-14y=48 therefore giving you 9y=-35 y=-35/9 then you simply substitute to any of the 2 equations 4x-5(-35/9)=13 4x= 13-175/9 = -58/9 x = -58/36 = -29/18 final answers: x = -29/18 y= -35/9 the answer is equal to the one which was arrived at using matrices.

Reference book (^.^) Simultaneous equations and Negative number [^1] = [ 3W + 2Y + Z = 39 ] [^2] = [ 2W + 3Y + Z = 34 ] [^3] = [ W + 2Y + 3Z = 26 ] (Image, .PNG) http://www.flickr.com/photos/trapassing/3547427977 http://www.flickr.com/photos/trapassing/3547427977/sizes/o/ (1) Explanation of Simultaneous equations ( 1 degree , 3 unknowns ) Purposefully, use negative number. (2) (Liuhui) (Chinese mathematician, about AD 220 ~ 280) [ Jiuzhangsuanshu-Fangchengzhang-Zhengfushu (Mathematics on nine chapters) ] [ Zhengfushu ] = [ Arithmetic on Positve, Zero, Negative / Addition(+), Subtraction(-) ] (3) Jiu = 9 zhang = Chapter suanshu = Mathematics Fangcheng = Equations zhang = Chapter Zheng = Positive number = Fortune number fu = Negative number = Debt number shu = Arithmetic (4) [^^^] = [ The Nine Chapters on the Mathematical Art ] = [ 9 Chapters Mathematics ] = [ Mathematics on nine chapters ] (5) (Source) http://www.nsc.gov.tw/sci/public/Attachment/69261610671.doc Subtraction (+a)-(+b)=+(a-b);(-a)-(-b)=-(a-b) (+a)-(-b)=+(a+b);(-a)-(+b)=-(a+b) 0-(+a)=-a;0-(-a)=+a Addition (+a)+(-b)=+(a-b);(-a)+(+b)=-(a-b) (+a)+(+b)=+(a+b);(-a)+(-b)=-(a+b) 0+(+a)=+a;0+(-a)=-a (6) 1. http://www.nsc.gov.tw/sci/public/Attachment/69261610671.doc 2. http://zh-classical.wikipedia.org/wiki/%E6%95%B4%E6%95%B8 3. http://www.chiculture.net/0803/html/c62/0803c62.html 4. http://www.seoprise.com/board/view.php?uid=4631&table=science (7) --- Start, Simultaneous equations ( 1 degree , 3 unknowns ) --- unhulled rice = UR hulled rice = HR 1 Mal = 18 Liter High grade = HG Average grade = AG Low grade = LG 1 bundle of unhulled rice = 1 BOUR 2 bundles of unhulled rice = 2 BOUR 3 bundles of unhulled rice = 3 BOUR [^^^] = [ (HG 3 BOUR) + (AG 2 BOUR) + (LG 1 BOUR) = HR 39 Mal ] [^^^] = [ (HG 2 BOUR) + (AG 3 BOUR) + (LG 1 BOUR) = HR 34 Mal ] [^^^] = [ (HG 1 BOUR) + (AG 2 BOUR) + (LG 3 BOUR) = HR 26 Mal ] [^^^] = [ (HG 1 BOUR) = (HR what Mal) = (W Mal) ] [^^^] = [ (AG 1 BOUR) = (HR what Mal) = (Y Mal) ] [^^^] = [ (LG 1 BOUR) = (HR what Mal) = (Z Mal) ] [^^^] = [ (HG 1 BOUR X 3) + (AG 1 BOUR X 2) + (LG 1BOUR X 1) = HR 39 Mal ] [^^^] = [ (HG 1 BOUR X 2) + (AG 1 BOUR X 3) + (LG 1BOUR X 1) = HR 34 Mal ] [^^^] = [ (HG 1 BOUR X 1) + (AG 1 BOUR X 2) + (LG 1BOUR X 3) = HR 26 Mal ] [^^^] = [ (W X 3) + (Y X 2) + (Z X 1) = 39 ] = [ W3 + Y2 + Z1 = 39 ] [^^^] = [ (W X 2) + (Y X 3) + (Z X 1) = 34 ] = [ W2 + Y3 + Z1 = 34 ] [^^^] = [ (W X 1) + (Y X 2) + (Z X 3) = 26 ] = [ W1 + Y2 + Z3 = 26 ] [^^^] = [ W3 + Y2 + Z1 = 39 ] = [ 3W + 2Y + 1Z = 39 ] [^^^] = [ W2 + Y3 + Z1 = 34 ] = [ 2W + 3Y + 1Z = 34 ] [^^^] = [ W1 + Y2 + Z3 = 26 ] = [ 1W + 2Y + 3Z = 26 ] [^^^] = [ 3W + 2Y + 1Z = 39 ] = [ (+3)W + (+2)Y + (+1)Z = (+39) ] [^^^] = [ 2W + 3Y + 1Z = 34 ] = [ (+2)W + (+3)Y + (+1)Z = (+34) ] [^^^] = [ 1W + 2Y + 3Z = 26 ] = [ (+1)W + (+2)Y + (+3)Z = (+26) ] [^^^] = [ + (+2) ] = [ (+2) ] = [ (2) ] = [ 2 ] [^^^] = [+ (+3) ] = [ (+3) ] = [ (3) ] = [ 3 ] [^^^] = [ N X (-N) ] = [ - { N X N } ], [ N X (+N) ] = [ + { N X N } ] [^1] = [ (+3)W + (+2)Y + (+1)Z = (+39) ] [^2] = [ (+2)W + (+3)Y + (+1)Z = (+34) ] [^3] = [ (+1)W + (+2)Y + (+3)Z = (+26) ] [^4] = [ (+3)W + (+2)Y + (+1)Z = (+39) ], [ (+2)W + (+3)Y + (+1)Z = (+34) ] = [ (+1)Z = (+39) - (+3)W - (+2)Y ], [ (+1)Z = (+34) - (+2)W - (+3)Y ] = [ (+39) - (+3)W - (+2)Y = (+1)Z ], [ (+1)Z = (+34) - (+2)W - (+3)Y ] = [ (+39) - (+3)W - (+2)Y = (+1)Z = (+34) - (+2)W - (+3)Y ] = [ (+39) - (+3)W - (+2)Y = (+34) - (+2)W - (+3)Y ] = [ (+2)W - (+3)W + (+3)Y- (+2)Y = (+34) - (+39) ] = [ (+2)W + (-3)W + (+3)Y- (+2)Y = (+34) - (+39) ] = [ (-3)W + (+2)W + (+3)Y- (+2)Y = (+34) - (+39) ] = [ (-3)W - (-2)W + (+3)Y- (+2)Y = (+34) - (+39) ] = [ (-1)W + (+3)Y- (+2)Y = (+34) - (+39) ] = [ (-1)W + (+1)Y = (+34) - (+39) ] = [ (-1)W - (-1)Y = (+34) - (+39) ] = [ (-1) X ( W - Y ) = (+34) - (+39) ] = [ (-1) X ( W - Y ) = (+34) + (-39) ] = [ (-1) X ( W - Y ) = (-39) + (+34) ] = [ (-1) X ( W - Y ) = (-39) - (-34) ] = [ (-1) X ( W - Y ) = (-5) ] = [ { (-1) X ( W - Y ) } X (-1) = (-5) X (-1) ] = [ (-1) X (-1) X ( W - Y ) = (-5) X (-1) ] = [ (+1) X ( W - Y ) = (+5) ] = [ (1) X ( W - Y ) = (5) ] = [ 1 X ( W - Y ) = 5 ] = [ W - Y = 5 ] [^5] = [ (+3)W + (+2)Y + (+1)Z = (+39) ] = [ { (+3)W + (+2)Y + (+1)Z } = (+39) ] = [ { (+3)W + (+2)Y + (+1)Z } X 3 = (+39) X 3 ] = [ { (+9)W + (+6)Y + (+3)Z } = (+117) ] = [ (+9)W + (+6)Y + (+3)Z = (+117) ] [^6] = [ (+9)W + (+6)Y + (+3)Z = (+117) ], [ (+1)W + (+2)Y + (+3)Z = (+26) ] = [ (+3)Z = (+117) - (+9)W - (+6)Y ], [ (+3)Z = (+26) - (+1)W - (+2)Y ] = [ (+117) - (+9)W - (+6)Y = (+3)Z ], [ (+3)Z = (+26) - (+1)W - (+2)Y ] = [ (+117) - (+9)W - (+6)Y = (+3)Z = (+26) - (+1)W - (+2)Y ] = [ (+117) - (+9)W - (+6)Y = (+26) - (+1)W - (+2)Y ] = [ (+1)W - (+9)W + (+2)Y - (+6)Y = (+26) - (+117) ] = [ (+1)W + (-9)W + (+2)Y - (+6)Y = (+26) - (+117) ] = [ (-9)W + (+1)W + (+2)Y - (+6)Y = (+26) - (+117) ] = [ (-9)W - (-1)W + (+2)Y - (+6)Y = (+26) - (+117) ] = [ (-8)W + (+2)Y - (+6)Y = (+26) - (+117) ] = [ (-8)W + (+2)Y + (-6)Y = (+26) - (+117) ] = [ (-8)W + (-6)Y + (+2)Y = (+26) - (+117) ] = [ (-8)W + (-6)Y - (-2)Y = (+26) - (+117) ] = [ (-8)W + (-4)Y = (+26) - (+117) ] = [ (-1) X (+8)W + (-1) X (+4)Y = (+26) - (+117) ] = [ (-1) X { (+8)W + (+4)Y } = (+26) - (+117) ] = [ (-1) X { (+8)W + (+4)Y } = (+26) + (-117) ] = [ (-1) X { (+8)W + (+4)Y } = (-117) + (+26) ] = [ (-1) X { (+8)W + (+4)Y } = (-117) - (-26) ] = [ (-1) X { (+8)W + (+4)Y } = (-91) ] = [ < (-1) X { (+8)W + (+4)Y } > X (-1) = (-91) X (-1) ] = [ (-1) X (-1) X { (+8)W + (+4)Y } = (-91) X (-1) ] = [ (+1) X { (+8)W + (+4)Y } = (+91) ] = [ (1) X { (8)W + (4)Y } = (91) ] = [ 1 X { 8W + 4Y } = 91 ] = [ 8W + 4Y = 91 ] [^7] = [ W - Y = 5 ] = [ ( W - Y ) = 5 ] = [ ( W - Y ) X 4 = 5 X 4 ] = [ 4W - 4Y = 20 ] [^8] = [ 8W + 4Y = 91 ], [ 4W - 4Y = 20 ] = [ 4Y = 91 - 8W ], [ 4W - 20 = 4Y ] = [ 91 - 8W = 4Y ], [ 4Y = 4W - 20 ] = [ 91 - 8W = 4Y = 4W - 20 ] = [ 91 - 8W = 4W - 20 ] = [ 91 + 20 = 4W + 8W] = [ 111 = 12W] = [ 111/12 = W] = [ 9.25 = W] = [ W = 9.25 ] = [ W = 9.25 Mal] [^9] = [ W - Y = 5 ] = [ 9.25 - Y = 5 ] = [ 9.25 - 5 = Y ] = [ 4.25 = Y ] = [ Y = 4.25 ] = [ Y = 4.25 Mal ] [^10] = [ (+3)W + (+2)Y + (+1)Z = (+39) ] = [ (3)W + (2)Y + (1)Z = (39) ] = [ 3W + 2Y + 1Z = 39 ] = [ 3W + 2Y + Z = 39 ] = [ ( 3 X 9.25 ) + ( 2 X 4.25) + Z = 39 ] = [ ( 3 X 9.25 ) + ( 2 X 4.25) + Z = 39 ] = [ (27.75) + (8.5) + Z = 39 ] = [ 36.25 + Z = 39 ] = [ Z = 39 - 36.25 ] = [ Z = 2.75 ] = [ Z = 2.75 Mal ] --- End, Simultaneous equations ( 1 degree , 3 unknowns ) ---

4x-5y=13 -------------- a 2x-7y=24 -------------- b a-2b: (4x-5y)-(4x-14y) = 13-48 -5y+14y = -35 9y = -35 y = -35/9 sub y = -35/9 in to b: 2x-(7)(-35/9) = 24 2x = -29/9 x = -29/18 Ans: x = -29/18, y = -35/9

4x - 5y = 13 2x - 7y = 24 Using graphical method! Draw the line y=4/5x-13/5 and y=2/7x-24/7 on the same cartesian plane and the (x,y) coordinates where the two lines meet are the x and y solutions respectively.