第43页 - 伴你学活页卷七年级数学苏科版

 解：将$y = x - 4$代入$x + y = 6，$得$x + (x - 4)=6，$$2x - 4 = 6，$$2x = 10，$解得$x = 5。$把$x = 5$代入$y = x - 4，$得$y = 5 - 4 = 1。$所以方程组的解为$\begin{cases}x = 5 \\ y = 1\end{cases}$

 解：由$x - 3y = -2$可得$x = 3y - 2，$将其代入$2x + y = 3，$得$2(3y - 2)+y = 3，$$6y - 4 + y = 3，$$7y = 7，$解得$y = 1。$把$y = 1$代入$x = 3y - 2，$得$x = 3×1 - 2 = 1。$所以方程组的解为$\begin{cases}x = 1 \\ y = 1\end{cases}$

 解：$\begin{cases}5x - 6y = 9&① \\ 7x - 4y = -5&②\end{cases}，$$①×2$得$10x - 12y = 18$  $③，$$②×3$得$21x - 12y = -15$  $④，$$④ - ③$得：$21x - 12y-(10x - 12y)=-15 - 18，$$21x - 12y - 10x + 12y=-33，$$11x = -33，$解得$x = -3。$把$x = -3$代入$①$得：$5×(-3)-6y = 9，$$-15 - 6y = 9，$$-6y = 24，$解得$y = -4。$所以方程组的解为$\begin{cases}x = -3 \\ y = -4\end{cases}$

 解：$\begin{cases}2x + 2y+z = 6&① \\ x - y + 2z = -1&② \\ x + 2y - z = 5&③\end{cases}，$$①+③$得：$2x + 2y+z+x + 2y - z = 6 + 5，$$3x + 4y = 11$  $④；$$①×2 - ②$得：$2(2x + 2y+z)-(x - y + 2z)=2×6-(-1)，$$4x + 4y + 2z - x + y - 2z = 12 + 1，$$3x + 5y = 13$  $⑤；$$⑤ - ④$得：$3x + 5y-(3x + 4y)=13 - 11，$$y = 2。$把$y = 2$代入$④$得：$3x + 4×2 = 11，$$3x = 3，$解得$x = 1。$把$x = 1，$$y = 2$代入$①$得：$2×1 + 2×2+z = 6，$$z = 0。$所以方程组的解为$\begin{cases}x = 1 \\ y = 2 \\ z = 0\end{cases}$

 解：联立$\begin{cases}2x + 5y = -6 \\ 3x - 5y = 16\end{cases}，$两式相加得：$2x + 5y+3x - 5y=-6 + 16，$$5x = 10，$解得$x = 2。$把$x = 2$代入$2x + 5y = -6$得：$2×2 + 5y = -6，$$5y = -10，$解得$y = -2。$把$\begin{cases}x = 2 \\ y = -2\end{cases}$代入$\begin{cases}ax - by = -4 \\ bx + ay = -8\end{cases}$得$\begin{cases}2a + 2b = -4 \\ 2b - 2a = -8\end{cases}，$两式相加得$4b = -12，$解得$b = -3；$两式相减得$4a = 4，$解得$a = 1。$所以$(2a + b)^{2024}=(2×1-3)^{2024}=(-1)^{2024}=1。$