Question

x + y = 5
-3x + y = -2
x - y = 7

Explanation:

Step1: Subtract the second equation from the first

$(x + y)-(-3x + y)=5-(-2)$
$x + y + 3x - y=5 + 2$
$4x=7$
$x=\frac{7}{4}$

Step2: Substitute $x$ into the first equation

$\frac{7}{4}+y = 5$
$y=5-\frac{7}{4}$
$y=\frac{20 - 7}{4}=\frac{13}{4}$

Step3: Check with the third equation

Left - hand side of $x - y$: $\frac{7}{4}-\frac{13}{4}=\frac{7 - 13}{4}=-\frac{6}{4}=-\frac{3}{2}
eq7$
Since the values of $x$ and $y$ obtained from the first two - equations do not satisfy the third equation, this system of equations has no solution.

Answer:

No solution