This animation walks through finding unknown coefficients a and b in a pair of linear equations, given that the system has a known solution point (2, -1). It shows how substituting the known x and y values into each equation isolates the unknown coefficient, turning the problem into simple one-variable algebra. The final step combines both results to compute a minus b. Useful for students learning substitution techniques and solving for parameters in linear equations.
Narrated · 16:9 · Preview before teaching · automatic layout checks do not establish subject accuracy
Pembahasan Diketahui sistem persamaan: \[ 4x+ay=14 \] \[ bx-3y=11 \] Mempunyai solusi: \[ (x,y)=(2,-1) \] Artinya, \(x=2\) dan \(y=-1\). Ditanya: Nilai \(a-b\) adalah .... Langkah 1: Menentukan nilai \(a\) Gunakan persamaan pertama: \[ 4x+ay=14 \] Substitusikan \(x=2\) dan \(y=-1\): \[ 4(2)+a(-1)=14 \] \[ 8-a=14 \] Pindahkan 8 ke ruas kanan: \[ -a=14-8 \] \[ -a=6 \] Kalikan kedua ruas dengan \(-1\): \[ \boxed{a=-6} \] Langkah 2: Menentukan nilai \(b\) Gunakan persamaan kedua: \[ bx-3y=11 \] Substitusikan \(x=2\) dan \(y=-1\): \[ b(2)-3(-1)=11 \] \[ 2b+3=11 \] Pindahkan 3 ke ruas kanan: \[ 2b=11-3 \] \[ 2b=8 \] Bagi kedua ruas dengan 2: \[ \boxed{b=4} \] Langkah 3: Menghitung nilai \(a-b\) Diketahui: \[ a=-6,\qquad b=4 \] Maka: \[ a-b=-6-4 \] \[ \boxed{a-b=-10} \] Jadi, jawaban akhirnya adalah \(-10\).