Question

Solve the Linear System using the elimination method or the Substitution method

3x+4y=4
3x+y=10

Answer 1

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)

Answer 2

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

Answer 3

?

Answer 4

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.