Question

which systems of equations do not have any solutions? select all that apply. click or tap the correct systems of equations. x + y = 5\
x + y = 6\
x + y = 7\
x - y = 2\
3x + y = 6\
2x + y = 8\
6x + 2y = 12\
2x + y = 4

Explanation:

Step1: Analyze parallel line condition

A system of linear equations $a_1x+b_1y=c_1$ and $a_2x+b_2y=c_2$ has no solution if $\frac{a_1}{a_2}=\frac{b_1}{b_2}
eq\frac{c_1}{c_2}$ (parallel, non-overlapping lines).

Step2: Check first system

System: $x+y=5$, $x+y=7$
$\frac{1}{1}=\frac{1}{1}
eq\frac{5}{7}$ → No solution.

Step3: Check second system

System: $x+y=6$, $x-y=2$
$\frac{1}{1}
eq\frac{1}{-1}$ → Has a solution.

Step4: Check third system

System: $3x+y=6$, $2x+y=8$
$\frac{3}{2}
eq\frac{1}{1}$ → Has a solution.

Step5: Check fourth system

System: $6x+2y=12$, $2x+y=4$
Simplify first equation: $3x+y=6$. $\frac{3}{2}
eq\frac{1}{1}$? No, simplify ratios: $\frac{6}{2}=\frac{2}{1}=\frac{12}{4}=2$ → Lines are coincident, infinite solutions.

Answer:

The system with no solutions is:
$x + y = 5$ and $x + y = 7$