\( -3 x+8 y=7 \) \( -x+6 y=-1 \) Is \( (-5,-1) \) a solution to the system above? \( \bigcirc \) True \( \bigcirc \) False Submit Question

To determine if \( (-5, -1) \) is a solution to the system of equations, we can substitute \( x = -5 \) and \( y = -1 \) into both equations. For the first equation: \[ -3(-5) + 8(-1) = 15 - 8 = 7 \] This is true, so the first equation is satisfied. For the second equation: \[ -(-5) + 6(-1) = 5 - 6 = -1 \] This is also true, so the second equation is satisfied as well. Since both equations are satisfied, the answer is \( \bigcirc \) True. --- To see how systems of equations like this are used in the real world, think of them like balancing your checkbook. Each equation represents a financial condition you need to meet, such as spending limits and income. Finding a solution means identifying your income and spending in a way that satisfies all your financial obligations. When solving systems of equations, a common mistake is to miscalculate the substitution. Always double-check each step, as a small numerical error can lead to the wrong conclusion. Using a methodical approach, like graphing or elimination, can help avoid these pitfalls!