Question

Solve, using linear combination. a – 3b = – 12a + 3b = 16Which ordered pair, (a, b), is the solution to the system of equations?(5, 2)(11, 2)(11, 4)(10, 3)

Answer 1

The equations are

`\begin{bmatrix}a-3b=-1...........1 \\ 2a+3b=16..........2\end{bmatrix}`

Using Substitution method of simultaneous equation

Isolate for 'a' from equation 1

`a=-1+3b........3`

Therefore,

`\begin{gathered} \mathrm{Substitute\:}a=-1+3b \\ 2\left(-1+3b\right)+3b=16 \\ -2+9b=16 \\ 9b=16+2=18 \\ 9b=18 \\ b=(18)/(9)=2 \\ \therefore b=2 \end{gathered}`

Then

`\begin{gathered} \mathrm{For\:}a=-1+3b \\ \mathrm{Substitute\:}b=2 \\ a=-1+3\cdot\:2=-1+6=5 \\ \therefore a=5 \end{gathered}`

Hence, the answer is

`(a,b)=(5,2)`