Final answer:
To solve the system of equations -9x - 4y = 1 and 3x + 2y = 3, the method of substitution can be used. The solution to the system is x = -1 and y = 2.
Step-by-step explanation:
To solve the system of equations -9x - 4y = 1 and 3x + 2y = 3, we can use the method of substitution or elimination. Let's use the method of substitution:
Step 1: Solve one equation for one variable. Let's solve the second equation for x: 3x = 3 - 2y.
Step 2: Substitute the expression for x into the other equation: -9(3 - 2y) - 4y = 1.
Step 3: Simplify and solve for y: -27 + 18y - 4y = 1.
Step 4: Combine like terms: 14y = 28.
Step 5: Solve for y: y = 2.
Step 6: Substitute the value of y back into one of the original equations to solve for x: -9x - 4(2) = 1.
Step 7: Simplify and solve for x: -9x - 8 = 1.
Step 8: Combine like terms: -9x = 9.
Step 9: Solve for x: x = -1.
Therefore, the solution to the system of equations is x = -1 and y = 2.