x = 7 - 2y
3x = 21 - 6y
21 - 6y + 2y = 5
21 - 4y = 5
21 - 16 = 5
4y = 16
y = 4
x + 8 = 7
x = -1
Check it.
-3 + 8 = 5
-1 + 8 = 7
It checks.
I notice that the ratio of the y-coefficient to the x-coefficient is the same in both equations. I think that's enough to tell me that their graphs are parallel. So they don't intersect, and viewed as a pair of simultaneous equations, they have no solution.
Simultaneous equations: x/3 -y/4 = 0 and x/2 +3y/10 = 27/5 Multiply all terms in the 1st by 12 and in the 2nd equation by 10 So: 4x -3y = 0 and 5x +3y = 54 Add both equations together: 9x = 54 => x = 6 Solutions by substitution: x = 6 and y = 8
Solving the above simultaneous equations by means of the elimination method works out as x = 2 and y = 3
If: 3x+2y = 5x+2y = 14 Then: 3x+2y = 14 and 5x+2y =14 Subtract the 1st equation from the 2nd equation: 2x = 0 Therefore by substitution the solutions are: x = 0 and y = 7
The two equations represent the same straight line.
Through a process of elimination and substitution the solutions are s = 8 and x = 5
They are simultaneous equations and their solutions are x = 41 and y = -58
The solutions are: x = 4, y = 2 and x = -4, y = -2
Simultaneous equations.
If: 2x+y = 5 and x2-y2 = 3 Then the solutions work out as: (2, 1) and ( 14/3, -13/3)
These are two expressions, not equations. Expressions do not have solutions, only equations do. NB equations include the equals sign.
Another straight line equation is needed such that both simultaneous equations will intersect at one point.
1
The solutions work out as: x = 52/11, y = 101/11 and x = -2, y = -11
I notice that the ratio of the y-coefficient to the x-coefficient is the same in both equations. I think that's enough to tell me that their graphs are parallel. So they don't intersect, and viewed as a pair of simultaneous equations, they have no solution.
Without any equality signs the given expressions can't be considered to be simultaneous equations and so therefore no solutions are possible.
Just one.