Question

Which system of equations has no solution?

5 x + 5 y = 10 and 2 x + 2 y = 4
3 x minus 6 y = 4 and negative 4 x + 8 y = 7
6 x + 2 y = 6 and 7 x + 3 y = 9
3 x minus 4 y = 16 and 2 x + 3 y = 5

Answer 1

The system of the equation; 5 x + 5 y = 10 and 2 x + 2 y = 4 has no solution

Explanation:

Let's check the first equation and see

5x + 5y = 10 ------------------------------------------------------------------------(1)

2x + 2y = 4 -------------------------------------------------------------------------(2)

Using elimination method,

Multiply through equation (1) by 2 and multiply through equation(2) by 5

10x + 10y = 20 ----------------------------------------------------------------------(3)

10x + 10y = 20 ---------------------------------------------------------------------(4)

When we subtract equation (3) from (4), both the x and y variables will go away.

Therefore this system of equation has no solution.

Answer 2

The system of equation 5x+5y=10 and 2x+2y=4 has no solution.

The system of equation 3x-6y=4 and -4x+8y=7 has no solution.

Explanation:

The set of equations "which cannot be solved for X and Y values is said to have no solution".

Now, let's try to solve the following sets of equations for x and y values to find which system of equation has no solution.

option 1:

divide the 1st equation by 5,

the equation becomes x+y=2

divide the 2nd equation by 2,

the equation becomes x+y=2

Both the equations are same, it cannot be solved and has no solution.

option 2:

look for the least coefficients of x and y to make multiplication easy

so, the coefficients of x are 3 and 4.

multiply equation1 by 4

the 1st eqn becomes 12x-24y=16

multiply euation2 by 3

the 2nd eqn becomes -12x+24y=21

Try to solve these two equation for x and y values.

since they cannot be solved to x and y values, it has No solution

Similarly the options 3 and 4 is to be solved to find either it has solution or not.

After solving option 3, the solution is x=0 and y=3

After solving option 4, the solution is x=4 and y=-1