x = y + 1 so 8 (y + 1) + 3y = 4, ie 8y + 8 + 3y = 4 ie 11y = -4 so y = -4/11 and x = 7/11
Check: 56/11 - 12/11 = 44/11 = 4 QED
Another explanation:
This is a simultaneous equation and can be solved using the elimination method in the form of:
8x+3y = 4
3(x-y = 1)
Multiply all terms in the bottom equation by 3:
8x+3y = 4
3x-3y = 3
Add both equations together in order to eliminate y:
11x = 7
Divide both sides by 11 to find the value of x:
x = 7/11
Substitute the value of x into the original equations to find the value of y:
Therefore: x = 7/11 and y = -4/11
Proof: If x-y = 1 then 7/11 - - 4/11 = 1 (remember that in maths a - - equals +)
x+3y=2 x= -5 y = 1
x = 5, y = -1
Yes and it works out that x = 3 and y = 4
y=16 x= -4
2x + 3y = 9x = 3, y = 1 therefore 6 + 3 = 9
(3,3)
Solve this system of equations. 5x+3y+z=-29 x-3y+2z=23 14x-2y+3z=-18 Write the solution as an ordered triple.
x+3y=2 x= -5 y = 1
5y = 3y + 12 5y - 3y = (3y - 3y) + 12 2y = 12 y = 6
10y= 6y+5+3y 10y=6+9y y=6
x = 5, y = -1
3y + 8 = 3 -8 -8 3y=-5 (3y)/3=-5/3 y=(-5/3)
3y + 2y + 4 + 1 = 805y + 5 = 805y = 75y = 15
Yes and it works out that x = 3 and y = 4
80 = 3y + 2y + 4 + 1 75 = 5y 15 = y y = 15
y=16 x= -4
2x + 3y = 9x = 3, y = 1 therefore 6 + 3 = 9