Question

Solve for x and y:3x+4y=9,2x+3y=8

Answer 1

Answer on Question #58788– Math– Algebra

Question

Solve for $x$ and $y$:

$$3x + 4y = 9, 2x + 3y = 8.$$

Solution

We have the system of linear equations

$$\left\{ \begin{array}{l} 3x + 4y = 9 \\ 2x + 3y = 8 \end{array} \right.$$

Expressing $x$ from the first equation of (1) and substituting for $x$ into the second equation of (1) we obtain

$$\begin{aligned} \left\{ \begin{array}{l} 3x = 9 - 4y \\ 2x + 3y = 8 \end{array} \right. & \Rightarrow \left\{ \begin{array}{l} x = \frac{9 - 4y}{3} \\ 2x + 3y = 8 \end{array} \right. \Rightarrow \left\{ \begin{array}{l} x = \frac{9 - 4y}{3} \\ 2 \frac{9 - 4y}{3} + 3y = 8 \end{array} \right. \Rightarrow \left\{ \begin{array}{l} x = \frac{9 - 4y}{3} \\ 2(9 - 4y) + 9y = 24 \end{array} \right. \Rightarrow \\ & \Rightarrow \left\{ \begin{array}{l} x = \frac{9 - 4y}{3} \\ 18 - 8y + 9y = 24 \end{array} \right. \Rightarrow \left\{ \begin{array}{l} x = \frac{9 - 4y}{3} \\ y = 6 \end{array} \right. \Rightarrow \left\{ \begin{array}{l} x = \frac{9 - 4 \cdot 6}{3} \\ y = 6 \end{array} \right. \Rightarrow \left\{ \begin{array}{l} x = \frac{-15}{3} \\ y = 6 \end{array} \right. \Rightarrow \left\{ \begin{array}{l} x = -5 \\ y = 6. \end{array} \right. \end{aligned}$$

Answer: $x = -5, y = 6$.

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