All you need to do on these is make the coefficient(number) of either variable the same, usually by multiplication, then add or subtract to eliminate that variable.
Using Y
As the coefficients of Y are the same, just add the equations:
3x - 2y = 11
x + 2y = 9
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4x + 0y = 20
4x = 20 , which means X = 5 and Y =2
Using X
3x - 2y = 11
x + 2y = 9
Multiply the second equation by 3 and subtract.
x + 2y = 9 becomes 3x + 6y = 27, and it is easiest to just subtract the first
3x + 6y = 27
- (3x - 2y = 11)
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0x +8y = 16
8y = 16 so Y = 2 and X = 5
Simultaneous equations.
The system is simultaneous linear equations
Another straight line equation is needed such that both simultaneous equations will intersect at one point.
It's a simultaneous equation and can be solved by elimination which works out as:- x = -4 and y = 1
By elimination: x = 3 and y = 0
The elimination method only works with simultaneous equations, hence another equation is needed here for it to be solvable.
Through a process of elimination and substitution the solutions are s = 8 and x = 5
Solving these simultaneous equations by the elimination method:- x = 1/8 and y = 23/12
Solving the above simultaneous equations by means of the elimination method works out as x = 2 and y = 3
Simultaneous suggests at least two equations.
Simultaneous equations.
The system is simultaneous linear equations
x = -3 y = -2
Solve this simultaneous equation using the elimination method after rearraging these equations in the form of: 3x-y = 5 -x+y = 3 Add both equations together: 2x = 8 => x = 4 Substitute the value of x into the original equations to find the value of y: So: x = 4 and y = 7
The point of intersection of the given simultaneous equations of y = 4x-1 and 3y-8x+2 = 0 is at (0.25, 0) solved by means of elimination and substitution.
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.
Another straight line equation is needed such that both simultaneous equations will intersect at one point.