2x+4y=20 3x+2y=26

Question

Just to know what the answer is

Answer 1

The first equation can be reduced: x+2y=10 so 2y=10-x.

The second equation can be rearranged: 2y=26-3x.

So we have 2y on the left of each so the right hand sides are equal:

26-3x=10-x, 16=2x so x=8 and 2y=10-8=2 so y=1.

The solution is x=8 and y=1 which satisfy both equations.

Answer 2

2X + 4Y = 20

3X + 2Y = 26

SOLUTION

2X + 4Y =20             *2

3X +2Y = 26            *4

SOLUTION CONTINUES

4X + 8Y = 40

12 + 8Y = 104

MULTIPLY EQUATION 2 THROUGH BY -

4X + 8Y = 40

-12X -8Y =-104

-8X = -64

DIVIDE BOTH SIDES BY -8

X = -64\-8

X =8

SUBSTITUTE X=8 IN EQUATION 1

2X + 4Y = 20 

2[8] + 4Y = 20 

16 + 4Y = 20

COLLECT LIKE TERMS 

4Y =20 - 16

4Y = 4

DIVIDE BOTH SIDES BY 4

Y =4\4

Y =1

[X,Y] [8,1]