if 7x+5y=107 and 5x+7y=77 then the value of XY

asked by guest
on Mar 15, 2025 at 8:40 am



You asked:

Given the following equations: 7x+5y=1075x+7y=77\begin{aligned}7 x + 5 y &= 107\\ 5 x + 7 y &= 77\end{aligned} Evaluate XYX Y.

MathBot Answer:

Assuming XX and xx are referring to the same variable.

Assuming YY and yy are referring to the same variable.


The system of linear equations has exactly one solution.

The substitutions are x=916 x = \frac{91}{6} , y=16 y = \frac{1}{6} .

XY=9136X Y = \frac{91}{36}


Solve 7x+5y=1077 x + 5 y = 107 for xx. x=10775y7x = \frac{107}{7} - \frac{5 y}{7}

Substitute 10775y7\frac{107}{7} - \frac{5 y}{7} for xx in 5x+7y=775 x + 7 y = 77 and simplify. 5x+7y=775(10775y7)+7y=77y=16\begin{aligned}5 x + 7 y &= 77 \\ 5 \left(\frac{107}{7} - \frac{5 y}{7}\right) + 7 y &= 77 \\ y &= \frac{1}{6} \end{aligned}

Use substitution of the numerical value of yy to get the values of xx. x=10775y7x=1567+1077x=916\begin{aligned}x &= \frac{107}{7} - \frac{5 y}{7} \\ x &= - \frac{1 \cdot 5}{6 \cdot 7} + \frac{107}{7} \\ x &= \frac{91}{6}\end{aligned}

By substituting these values into the expression, we find that:XY=91616=9136\begin{aligned} X Y &= \frac{91}{6} \cdot \frac{1}{6}\\ &=\frac{91}{36}\end{aligned}