which ordered pair (p, r) is the solution to the given system of linear equations?\n\\begin{cases}5p - 3r =…

which ordered pair (p, r) is the solution to the given system of linear equations?\n\\begin{cases}5p - 3r = 1\\\\8p + 6r = 4\\end{cases}\n\\bigcirc\\ (-1, -2)\n\\bigcirc\\ (-2, -1)\n\\bigcirc\\ \\left(\\frac{2}{9}, \\frac{1}{3}\\right)\n\\bigcirc\\ \\left(\\frac{1}{3}, \\frac{2}{9}\\right)

which ordered pair (p, r) is the solution to the given system of linear equations?\n\\begin{cases}5p - 3r = 1\\\\8p + 6r = 4\\end{cases}\n\\bigcirc\\ (-1, -2)\n\\bigcirc\\ (-2, -1)\n\\bigcirc\\ \\left(\\frac{2}{9}, \\frac{1}{3}\\right)\n\\bigcirc\\ \\left(\\frac{1}{3}, \\frac{2}{9}\\right)

Answer

Explanation:

Step1: Multiply the first equation

To eliminate ( r ), multiply the first equation ( 5p - 3r = 1 ) by 2. We get ( 10p - 6r = 2 ).

Step2: Add the two equations

Now add the new first equation ( 10p - 6r = 2 ) and the second equation ( 8p + 6r = 4 ). So, ((10p - 6r)+(8p + 6r)=2 + 4), which simplifies to ( 18p=6 ).

Step3: Solve for ( p )

Divide both sides of ( 18p = 6 ) by 18. We get ( p=\frac{6}{18}=\frac{1}{3} ).

Step4: Substitute ( p ) into the first equation

Substitute ( p = \frac{1}{3} ) into ( 5p - 3r = 1 ). So, ( 5\times\frac{1}{3}-3r = 1 ), which is ( \frac{5}{3}-3r = 1 ).

Step5: Solve for ( r )

Subtract ( \frac{5}{3} ) from both sides: ( - 3r=1-\frac{5}{3}=\frac{3 - 5}{3}=-\frac{2}{3} ). Then divide by - 3: ( r=\frac{-\frac{2}{3}}{-3}=\frac{2}{9} ).

Answer:

(\left(\frac{1}{3},\frac{2}{9}\right))