Jom Cuba 3.1 [Soalan 3(e) & 3(f)] – Buku Teks Matematik Tingkatan 2 Bab 3 (Rumus Algebra)

Soalan 3(e):
Selesaikan yang berikut.
Diberi 3u = 4r + s, hitung
(i) nilai u apabila r = 5 dan s = −2
(ii) nilai r apabila u = 3 dan s = 3
(iii) nilai s apabila u = 2 dan r = ½

Penyelesaian:
(e)(i)
$$\begin{aligned} &\text { nilai } u \text { apabila } r=5 \text { dan } s=-2\\ &\begin{aligned} 3 u & =4 r+s \\ 3 u & =4(5)+(-2) \\ 3 u & =18 \\ u & =\frac{18}{3} \\ u & =6 \end{aligned} \end{aligned}$$


(e)(ii)
$$\begin{aligned} \text { nilai } r & \text { apabila } u=3 \text { dan } s=3 \\ 3 u & =4 r+s \\ 3(3) & =4 r+3 \\ 9-3 & =4 r \\ 6 & =4 r \\ \frac{6}{4} & =r \\ \frac{3}{2} & =r \\ r & =\frac{3}{2} \end{aligned}$$


(e)(iii)
$$\begin{aligned} &\text { nilai } s \text { apabila } u=2 \text { dan } r=\frac{1}{2}\\ &\begin{aligned} 3 u & =4 r+s \\ 3(2) & =4\left(\frac{1}{2}\right)+s \\ 6 & =2+s \\ 4 & =s \\ s & =4 \end{aligned} \end{aligned}$$

Soalan 3(f):
Selesaikan yang berikut.
$$\text { Diberi } \frac{3}{5} p=\frac{2}{3} q-\frac{1}{4} r \text {, hitung }$$
(i) nilai p apabila q = 3 dan r = 8
(ii) nilai q apabila r = −12 dan p = 10
(iii) nilai r apabila p = −15 dan q = −15

Penyelesaian:
(f)(i)
$$\begin{aligned} &\text { nilai } p \text { apabila } q=3 \text { dan } r=8\\ &\begin{aligned} \frac{3}{5} p & =\frac{2}{3} q-\frac{1}{4} r \\ \frac{3}{5} p & =\frac{2}{3}(3)-\frac{1}{4}(8) \\ \frac{3}{5} p & =2-2 \\ \frac{3}{5} p & =0 \\ p & =0 \end{aligned} \end{aligned}$$


(f)(ii)
$$\begin{aligned} & \text { nilai } q \text { apabila } r=-12 \text { dan } p=10 \\ & \begin{aligned} \frac{3}{5} p & =\frac{2}{3} q-\frac{1}{4} r \\ \frac{3}{5}(10) & =\frac{2}{3} q-\frac{1}{4}(-12) \\ 6 & =\frac{2}{3} q+3 \\ 3 & =\frac{2}{3} q \\ 3\left(\frac{3}{2}\right) & =q \\ \frac{9}{2} & =q \\ q & =\frac{9}{2} \end{aligned} \end{aligned}$$


(f)(iii)
$$\begin{aligned} &\text { nilai } r \text { apabila } p=-15 \text { dan } q=-15\\ &\begin{aligned} \frac{3}{5} p & =\frac{2}{3} q-\frac{1}{4} r \\ \frac{3}{5}(-15) & =\frac{2}{3}(-15)-\frac{1}{4} r \\ -9 & =-10-\frac{1}{4} r \\ \frac{1}{4} r & =-10+9 \\ \frac{1}{4} r & =-1 \\ r & =(-1)(4) \\ r & =-4 \end{aligned} \end{aligned}$$