what is the solution (a, c) to this system of linear equations? 2a - 3c = -6 a + 2c = 11 (-\\frac{76}{7}…

what is the solution (a, c) to this system of linear equations? 2a - 3c = -6 a + 2c = 11 (-\\frac{76}{7}, \\frac{17}{7}) (3, -4) (3, 4) (\\frac{87}{7}, -\\frac{5}{7})

what is the solution (a, c) to this system of linear equations? 2a - 3c = -6 a + 2c = 11 (-\\frac{76}{7}, \\frac{17}{7}) (3, -4) (3, 4) (\\frac{87}{7}, -\\frac{5}{7})

Answer

Explanation:

Step1: Multiply the second - equation

Multiply the equation $a + 2c=11$ by $2$ to get $2a+4c = 22$.

Step2: Subtract the first equation from the new equation

$(2a + 4c)-(2a-3c)=22-(-6)$. Simplify the left - hand side: $2a + 4c-2a + 3c=7c$. Simplify the right - hand side: $22 + 6=28$. So, $7c=28$, then $c = 4$.

Step3: Substitute $c = 4$ into the second equation

Substitute $c = 4$ into $a + 2c=11$, we get $a+2\times4=11$, which is $a + 8=11$. Solve for $a$: $a=11 - 8=3$.

Answer:

C. $(3,4)$