Explain how many solutions this system of equations has.

Question

asked Jun 17, 2023 164k views

1 Answer

Jared Dunham · Answer 1 · 2023-06-22T11:31:41+0000

Answer:

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.