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anonymous

  • one year ago

Solve the Linear System using the elimination method or the Substitution method 3x+4y=4 3x+y=10

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  1. anonymous
    • one year ago
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    Equations given are 4x = 3y + 4 ------------------->(1) 3x = 4y + 10 ------------------->(2) As, we see from equations (1) and (2) coefficients of x or y are not same. So, to make the coefficients of x same we multiply equation (1) by 3 and equation (2) by 4. 3(4x = 3y + 4) ------------>(1) 4(3x = 4y + 10) ------------->(2) We'll get 12x = 9y + 12 -------------------->(1) 12x = 16y + 40 -------------------->(2) Now, as you can see cofficients of x are same in both equations, but they both are positive. So, to eliminate x if we make one negative we'll eliminate x and we can then solve for y. To do that multiply equation (2) by -1 and then add. 12x = 9y + 12 ---------------(1) -1(12x = 16y + 40) -----------------(2) We'll get 12x = 9y + 12 -------------(1) -12x = -16y - 40 --------------(2) _______________ 0= -7y - 28 7y +7y (add 7y on both sides of equation) _________________ 7y = -28 (7y)/7 = -28/7 (divide both sides by 7) y =-4 (answer) Now, substitute the value of y in original equation (1) and solve for x. 4x = 3y + 4 (given equation) 4x = 3(-4) + 4 (since, y = 4) 4x = -12 + 4 4x = -8 (4x)/4 = -8/4 (divide both sides by 4) x = -2 (answer)

  2. anonymous
    • one year ago
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    this is a different way the i learned and much longer is there a different wayv

  3. anonymous
    • one year ago
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    ?

  4. anonymous
    • one year ago
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    You can also solve by using the Substitution method, if you prefer it. 3x+4y=4 3x+y=10 Since there is nothing being multiplied by y in the second equation, we'll solve for y there. It makes it easier because all we have to do is subtract 3x. 3x+4y=4 y=-3x+10 Since we have solved for y, you can plug in -3x+10 in the first equation. 3x+ 4(-3x+10)=4 Using the distributive property, we now get 3x-12x +40=4 Now combine like terms -9x=-36 And if we divide by -9 to solve for x, you see x=4. Now choose either of the equations and plug in 4 for x and solve for y.

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