Question

Which pair of equations is obtained by equating coefficients in \[5x-5=\mathrm{A}(x-3)+\mathrm{B}(x-2)\]?

Options

• \[\mathrm{A}+\mathrm{B}=5\] and \[3\mathrm{A}+2\mathrm{B}=5\]

• \[\mathrm{A}+\mathrm{B}=-5\] and \[3\mathrm{A}+2\mathrm{B}=5\]

• \[\mathrm{A}+\mathrm{B}=5\] and \[2\mathrm{A}+3\mathrm{B}=5\]

• \[\mathrm{A}-\mathrm{B}=5\] and \[3\mathrm{A}-2\mathrm{B}=5\]

Answer 1

Expanding gives \[(\mathrm{A}+\mathrm{B})x-(3\mathrm{A}+2\mathrm{B})\]. Matching the coefficients with \[5x-5\] gives the stated two equations.