Questions: If possible, solve the system of linear equations and check your answer. 8x+3y=-49 x+9y=37 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution is (Type an ordered pair.) B. There are infinitely many solutions. The solution set is (x, y) x+9y=37. C. There is no solution.

Solution Steps

To solve the system of linear equations, we can use the method of substitution or elimination. Here, we'll use the elimination method to eliminate one of the variables and solve for the other. Once we have the value of one variable, we substitute it back into one of the original equations to find the value of the other variable. Finally, we check the solution by substituting both values back into the original equations to ensure they satisfy both equations.

We are given the following system of linear equations: \[ \begin{align_} 8x + 3y &= -49 \\ x + 9y &= 37 \end{align_} \]

Using the elimination method, we solve for \(x\) and \(y\). The solution to the system is: \[ x = -8, \quad y = 5 \]

Substitute \(x = -8\) and \(y = 5\) back into the original equations to verify the solution:

1. For the first equation: \[ 8(-8) + 3(5) = -64 + 15 = -49 \] This satisfies the first equation.
2. For the second equation: \[ -8 + 9(5) = -8 + 45 = 37 \] This satisfies the second equation.

Final Answer