Mathematics
Grade-8
Easy
Question
Solve the following pair of equations.
- 2 x + 3 y= 12 and 4 x + 3 y = - 6
- 1, 3
- 1, 5
- 2, 5
- -3, 2
Hint:
The Linear Combination Method, aka The Addition Method , aka The Elimination Method. Add (or subtract) a multiple of one equation to (or from) the other equation, in such a way that either the x-terms or the y -terms cancel out. Then solve for x (or y, whichever's left) and substitute back to get the other coordinate.
The correct answer is: -3, 2
There are different methods for solving simultaneous linear Equations:
I. Elimination of a variable
II. Substitution
III. Cross-multiplication
IV. Evaluation of proportional value of variables
Here, we will be using Elimination of a variable method.
Here, we have 2 equations
- 2x + 3y= 12 can also be written as 2x - 3y = -12 (1)
4x + 3 y = -6 (2)
Multiplying 2 in equation(1), we get:
2 (2x - 3y = -12) = 4x -6y = -24 (3)
Subtracting equation 1 and 3 , we get :
4x - 6y = -24
-
4x +3y = -6
___________
= -9y = -18
y= 2
Substitute the value of y in equation (2), we get:
4x +3(2) = -6
x= -3
Thus, (x, y) = (-3, 2)
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![2 over x plus 3 over y equals 13 space a n d space 5 over x minus 4 over y equals negative 2](data:image/png;base64,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)
Solve the following pair of equations.
![2 over x plus 3 over y equals 13 space a n d space 5 over x minus 4 over y equals negative 2](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOMAAAAmCAYAAAA2qyxLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAABHNJREFUeNrtXWFkVWEY/lwzmcQk+9GPMUmSGUkmmUgmkxmTSZLRrySJfuRKEtOPSfYnyWQSM5NcE8lMMiMzk8kl/Ug/JiaTuSZu7+u8s6/Td+7utnvP9977PQ8P9347997vnPM+73nf97znmzHJOEWcIK4S14kLxEvGD84Qp4hrxAIxT3xM3G+AaqJYgr7Ro2QeqWCGOEDcK++PEj/KWNqYJvYRG62xDuJb6KXqYtQItsmlkMToQitxUdF8VqGXIMX4lDgYuhiNhIka0Eb8Ar0EJ0ZOn94rdxapoFNCVZ9oIV6VvPE89BKUGBslMmsNXYx7iHPimTQUE25CK6kc83VJB7iAdsuqIfjAEPF6DYTRVUUz8TXxnJK59Ipj6IJeUkED8TgxK6nBEQ9zaHdEZcGJsU2EeEjZvPaKIIF0wQ55xsPvzjlsMCgxsgd8RmxSOr8CtBHMcS8a3fc9qwoulIxLiKIRHLbkoYvUcYz4VVFOGwRynnIDFzgs6hfHkDFRR8434hVoo6qYNFEFPSPsFiH2QYx6woK0cVqcQ0HIHTk9Kc/hsBQwFhL+Xgste2siqnLRL/vxh7gikdIJZTZaK9DUXlrzGCNeK2EA2lv2uPixiNPoNbrT0l5aN2HFdvdBS8se3w56BU2ogtf20tDEWG7LHoeO94nLVgjTGtvmHvG2iQproxJycuh4w/F97H2fEH9JyMzh0QjxDuxfHQohirFoKlMeL2e77bbs5UQ8zSLMcbmS2RgX4bEQu2S7g3Iym2LCnpbf59f7RMhFx3eGhkrZQKXgtb203q+MO2nZGxCh2XjhEHFectY4+OpoF4myCVfAvIgX0IGS7aXFXbAanqjSc0nToWynZW9aPGQ82W+NXe1+Oz7bIOGqje/m//7RjGM72IC/q6uK9tJQwlQ7d9uqZS9+u8ElvJMiWleYY493GHerWtLnEaam78zVtJeGWE3dKkH/GXvPYcu8I5QdTQhx7XG+tTJWxnaAH6hqLw1NjOW07P2Q/MHO+SZi23BxZ9Dx2fh4ryP/NGbzHingD+raS+tZjDtt2XtgomUkMpInvjRRJ4+NSeOuysbH2eMuSbjK4MeeciJ4PIjtF5raS+sy37Cxm5a9u+I1s3KVXDb/3oZYiV09S423iEh5DrPiFJI+D+jIVwHFOIBDAAAAAAAAkASu0g0lFBwGPcznOfGiY5y7XB7idMEG6v1kzEtBYAPc7zjiaS5clXwUG+PqId86wDL/sIG6twF+sntYXp81m4vH+gCX5uP30LgBOgu9wAZCORnvTNRfueDZ+/Bvf7bec8WRl4BAyR42EIwNcDzOz9i1K5iL3ew8bLCQMWwgIBvYWLeDd3pAwXw+mKjRtk08YgY6gQ2EcBJ4Z99IgsxPH3xSkCTzc34XTNQydhk6gQ2EcBI4Fp+KHXhu7RpTEC5xeRsLK8EGgrABXt2MextdT4XzgkbdHufG/ZpF8YwAbADwCD4BszgMsAEcBv/gsKkThwE2gMPgF/w/HnI4DLCBet25v9U+r/u0dv1WAAABTnRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtZnJhYz48bW4+MjwvbW4+PG1pPng8L21pPjwvbWZyYWM+PG1vPis8L21vPjxtZnJhYz48bW4+MzwvbW4+PG1pPnk8L21pPjwvbWZyYWM+PG1vPj08L21vPjxtbj4xMzwvbW4+PG1vPiYjeEEwOzwvbW8+PG1pPmE8L21pPjxtaT5uPC9taT48bWk+ZDwvbWk+PG1vPiYjeEEwOzwvbW8+PG1mcmFjPjxtbj41PC9tbj48bWk+eDwvbWk+PC9tZnJhYz48bW8+LTwvbW8+PG1mcmFjPjxtbj40PC9tbj48bWk+eTwvbWk+PC9tZnJhYz48bW8+PTwvbW8+PG1vPi08L21vPjxtbj4yPC9tbj48L21hdGg+1fU53AAAAABJRU5ErkJggg==)
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Express x in terms of y.
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