Question

Solve algebraically
8x + 4y = 48
12x + 5y = 21

Answer 1

8x+4y=48
-4y -4y
8x=48-4y
divide 8 to both sides

x=6-1/2y


substitute the given value of x into the equation 12x+5y=21

12(6-1/2y)+5y=21

distribute 12 through the parentheses

72-6y+5y=21

add like terms

72-y=21

move constant to the right hand side and change signs

-y=21-72

calculate the difference

-y= -51

change signs

y=51

solve the question for x

x= 6-1/2 x 51

x= -39/2

(x,y) = (-39/2 , 51)

Answer 2

`x=-(39)/(2)\\ y=51`

Explanation:

`8x+4y=48\\12x+5y=21`

Let's solve the first equation for x or y. I'll do it for y.

`8x+4y=48`

Subtract 8x

`4y=-8x+48`

Divide by 4.

`y=-(8)/(4)x+(48)/(4)\\`

Simplify.

`y=-2x+12`

Now replace the value of y in the second equation for this.

`12x+5y=21\\12x+5(-2x+12)=21`

Distribute 5

`12x-10x+60=21`

Subtract 60

`12x-10x=21-60`

Combine like terms;

`2x=-39`

Divide by 2.

`x=-(39)/(2)`

Now replace this in any of the equations to find the value of y.

`8x+4y=48\\8(-(39)/(2))+4y=48\\`

8 and 2 can be simplified.

8/2=4

2/2=1

`4(-39)+4y=48`

Distribute 4.

`-156+4y=48`

Add 156

`4y=48+156\\4y=204`

Divide by 4

`y=(204)/(4)`

`y=51`

Proof:

`8x+4y=48\\8(-(39)/(2) )+4(51)=48\\4(-39)+204=48\\-156+204=48\\48=48`