解联立方程组。 $4m + 6n = 58$ $3m + 5n = 46$ 答案 m = ___ n = ___

1. Eliminate one variable by making the coefficients of $m$ equal.

$$\begin{aligned} 4m+6n&=58 \quad &(1)\\ 3m+5n&=46 \quad &(2) \end{aligned}$$

Multiply $(1)$ by $3$ and $(2)$ by $4$:

$$\begin{aligned} 12m+18n&=174\\ 12m+20n&=184 \end{aligned}$$

2. Subtract the equations to find $n$.

Subtract the first new equation from the second:

$$\begin{aligned} (12m+20n)-(12m+18n)&=184-174\\ 2n&=10\\ n&=5 \end{aligned}$$

3. Substitute $n$ back into one original equation to find $m$.

Substitute $n=5$ into $3m+5n=46$:

$$\begin{aligned} 3m+5(5)&=46\\ 3m+25&=46\\ 3m&=21\\ m&=7 \end{aligned}$$