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

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- anonymous

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

- katieb

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- anonymous

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)

- anonymous

this is a different way the i learned and much longer is there a different wayv

- anonymous

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- anonymous

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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