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What is the value of x and y.
2x - 3y = 2
,, 4x - 6y = 5

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Trinity academy

chaloner:
What is the value of x and y.
2x - 3y = 2
,, 4x - 6y = 5

................................................................
Trinity academy

The system is inconsistent.
If you multiply equation (1) by 2, you will get
4x - 6y = 4.
Comparing this with equation (2), the LHS of both equations are the same while their RHS are different. Hence they are inconsistent.

SirBrightoc:
The system is inconsistent.
If you multiply equation (1) by 2, you will get
4x - 6y = 4.
Comparing this with equation (2), the LHS of both equations are the same while their RHS are different. Hence they are inconsistent.

if what I have is inconsistent equation then , what will be its solution set? And of what form will the graph look like?

The answer would be x= 2 and y = 2/3 Iff the question says 2x - 3y = 2 , 4x - 6y = 4. Else the system is inconsistence cos d rank of the matrix formed from d homogeneous part of the equation doesn't equal to d rank of the argumented matrix formed from the non-homogeneous part of the equation (rank of d matrix = 1 while d rank of d argumented matrix = 2)

chaloner:
if what I have is inconsistent equation then , what will be its solution set? And of what form will the graph look like?

A system of equations is said to be inconsistent if the graphs can never meet and the equations contradict each other. Like in this case, 4x-6y can not be equal to 4 and at the same time equal to 5. Hence the equations have no solution.
Let me refer you to some websites to study more.

www.purplemath.com/modules/systlin2.htm

https://en.m.wikipedia.org/wiki/System_of_linear_equations

If we graph the two equations in this case, we will have two parallel lines. Observe that their slopes are equal if you write the equations in the form y + mx = c.

Quote me if you need additional explanation.

Gbengem:
The answer would be x= 2 and y = 2/3 Iff the question says 2x - 3y = 2 , 4x - 6y = 4. Else the system is inconsistence cos d rank of the matrix formed from d homogeneous part of the equation doesn't equal to d rank of the argumented matrix formed from the non-homogeneous part of the equation (rank of d matrix = 1 while d rank of d argumented matrix = 2)

Beloved, your first position is faulty as the equation 2x - 3y = 2 is also the same thing as 4x - 6y = 4 (obtained by multiplying the first equation by 2). Hence, the equation(s) has/have no unique solution.
Further observe that x = 1 and y = 0 will be another solution to the equation(s), even as there are uncountably many other possible solutions including (3, 4/3), (4, 2), (5, 8/3) etc. Note that all points on the line 2x - 3y = 2 will be the set of solutions.

SirBrightoc:
A system of equations is said to be inconsistent if the graphs can never meet and the equations contradict each other. Like in this case, 4x-6y can not be equal to 4 and at the same time equal to 5. Hence the equations have no solution.
Let me refer you to some websites to study more.

www.purplemath.com/modules/systlin2.htm

https://en.m.wikipedia.org/wiki/System_of_linear_equations

If we graph the two equations in this case, we will have two parallel lines. Observe that their slopes are equal if you write the equations in the form y + mx = c.

Quote me if you need additional explanation.

tnx so much. Its clean nd clear.

Gbengem:
The answer would be x= 2 and y = 2/3 Iff the question says 2x - 3y = 2 , 4x - 6y = 4. Else the system is inconsistence cos d rank of the matrix formed from d homogeneous part of the equation doesn't equal to d rank of the argumented matrix formed from the non-homogeneous part of the equation (rank of d matrix = 1 while d rank of d argumented matrix = 2)

I think that system of eqautions have no solution thus inconsistence as sirBright said. And that means that the solution set will be { } empty set. If ploted on the graph yields two parallel lines thus no point of intersection.