Question

Explain how many solutions this system of equations has.

Answer 1

No solution

Explanation:

`\rightarrow \left \{ {{2y = 6x + 4} \atop {y = 3x - 4}} \right. \\\\`

Multiply the second equation by 2 to make the "x" coordinates the same.

`\rightarrow \left \{ {{2y = 6x + 4} \atop {2(y = 3x - 4)}} \right. \\\\`

`\rightarrow \left \{ {{2y = 6x + 4} \atop {2y = 6x - 8}} \right. \\\\`

Subtract 6x from the first equation with the second equation

`\rightarrow \left \{ {{2y = 6x + 4} \atop {-2y = -6x + 8}} \right. \\\\`

`\rightarrow 0y = 0x + 12`

Simplify the R.H.S

`\rightarrow 0 \\eq 12`

This system of equation has no solution.

Graph: