Question

Solve the Equation
4x+3y=18
3x+4y=3

Answer 1

x = 9, y = -6

Explanation:

`\left\{\begin{array}{ccc}4x+3y=18&(1)\\3x+4y=3&(2)\end{array}\right\\\\(1)\\4x+3y=18\qquad\text{subtract}\ 4x\ \text{from both sides}\\3y=-4x+18\qquad\text{divide both sides by 3}\\y=-(4)/(3)x+6\qquad\text{substitute it in (2):}\\\\3x+4\left(-(4)/(3)x+6\right)=3\qquad\text{use the distributive property}\\\\3x+(4)\left(-(4)/(3)x\right)+(4)(6)=3\\\\3x-(16)/(3)x+24=3\qquad\text{multiply both sides by 3}\\\\9x-16x+72=9\qquad\text{subtract 72 from both sides}\\\\-7x=-63\qquad\text{divide both sides by (-7)}\\\\\boxed{x=9}`

`\text{Put the value of x to (1):}\\\\y=-(4)/(3)(9)+6\\\\y=(-4)(3)+6\\\\y=-12+6\\\\\boxed{y=-6}`

Answer 2

(9,-6)

Explanation:

4x+3y=18

3x+4y=3

Multiply the first equation by 3

3(4x+3y)=18*3

12x+9y = 54

Multiply the second equation by -4

-4(3x+4y)=3*-4

-12x -16y = -12

Add these two new equations together to eliminate x

12x+9y = 54

-12x -16y = -12

-----------------------

-7y = 42

Divide each side by -7

-7y/-7 = 42/-7

y = -6

Now we can find x

3x+4y =3

3x +4(-6) = 3

3x -24 =3

Add 24 to each side

3x-24+24 = 3+24

3x = 27

3x/3 = 27/3

x = 9

(9,-6)