Question

Which ordered pair is the solution to the system of equations below when using the matrix tool?6x + 4y = 303x+5y = 42A. (-3,7)B. (-1,9)C. (-4, 6)D. (-2,8)

Answer 1

Given

`\begin{gathered} 6x+4y=30 \\ 3x+5y=42 \end{gathered}`

To find:

Which ordered pair is the solution to the system of equations below when using the matrix tool?

Step-by-step explanation:

It is given that,

`\begin{gathered} 6x+4y=30 \\ 3x+5y=42 \end{gathered}`

That implies,

`\begin{gathered} [A,B]=\begin{bmatrix}{6} & {4} & |{30} \\ {3} & {5} & |{42} \\ {} & {} & {}\end{bmatrix} \\ =\begin{bmatrix}{3} & 2 & |{15} \\ {3} & {5} & |{42} \\ {} & {} & {}\end{bmatrix}[R_1\Rightarrow R_1/2] \\ =\begin{bmatrix}{3} & 2 & |{15} \\ 0 & {3} & |27 \\ {} & {} & {}\end{bmatrix}[R_2=R_2-R_1] \\ \end{gathered}`

Therefore,

`\begin{gathered} 3y=27\text{ \_\_\_\_\_\_\lparen1\rparen} \\ y=(27)/(3) \\ y=9 \\ 3x+2y=15\text{ \_\_\_\_\_\_\lparen2\rparen} \\ 3x+2(9)=15 \\ 3x+18=15 \\ 3x=15-18 \\ 3x=-3 \\ x=-1 \end{gathered}`

Hence, the solution set is (-1,9).