7x + 3y = 20 and –4x – 6y = 11. Find the value of 3x – 3y.

asked by guest
on Nov 20, 2024 at 8:34 am



You asked:

Given the following equations: \[\begin{aligned}7 x + 3 y &= 20\\ -\left( 4 x \right) - 6 y &= 11\end{aligned}\] Evaluate \(3 x - 3 y\).

MathBot Answer:

The system of linear equations has exactly one solution.

The substitutions are \( x = \frac{51}{10} \), \( y = - \frac{157}{30} \).

\[3 x - 3 y = 31\]

Solve \(7 x + 3 y = 20\) for \(x\). \[x = \frac{20}{7} - \frac{3 y}{7}\]

Substitute \(\frac{20}{7} - \frac{3 y}{7}\) for \(x\) in \(- 4 x - 6 y = 11\) and simplify. $$\begin{aligned}- 4 x - 6 y &= 11 \\ - 4 \left(\frac{20}{7} - \frac{3 y}{7}\right) - 6 y &= 11 \\ y &= - \frac{157}{30} \end{aligned}$$

Use substitution of the numerical value of \(y\) to get the values of \(x\). $$\begin{aligned}x &= \frac{20}{7} - \frac{3 y}{7} \\ x &= - \frac{\left(-157\right) 3}{7 \cdot 30} + \frac{20}{7} \\ x &= \frac{51}{10}\end{aligned}$$

By substituting these values into the expression, we find that:$$\begin{aligned} 3 x - 3 y &= 3 \cdot \frac{51}{10} - - \frac{157}{10}\\ &=31\end{aligned}$$

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