时间：2025-05-23 17:12
地点：万全区
To solve the system of equations x - 3y = 32 and x + y = -2, we can use the method of substitution or elimination. Method 1: Substitution Step 1: Solve one equation for one variable in terms of the other variable. From the second equation, we have x = -2 - y. Step 2: Substitute the expression for x into the other equation. In the first equation, replace x with -2 - y: (-2 - y) - 3y = 32. Step 3: Simplify and solve for y. -2 - y - 3y = 32 -2 - 4y = 32 -4y = 34 y = -34/4 y = -17/2 Step 4: Substitute the value of y back into one of the original equations to solve for x. Using the second equation: x + (-17/2) = -2 x - 17/2 = -2 x = -2 + 17/2 x = -4/2 + 17/2 x = 13/2 So the solution to the system of equations is x = 13/2 and y = -17/2. Method 2: Elimination Step 1: Multiply the second equation by 3 to make the coefficients of y in both equations equal. Original equations: x - 3y = 32 and x + y = -2. After multiplying the second equation by 3: 3x + 3y = -6. Step 2: Add the two equations together to eliminate the y terms. (x - 3y) + (3x + 3y) = 32 + (-6) 4x = 26 x = 26/4 x = 13/2 Step 3: Substitute the value of x into one of the original equations and solve for y. Using the second equation: (13/2) + y = -2 y = -2 - 13/2 y = -4/2 - 13/2 y = -17/2 So the solution to the system of equations is x = 13/2 and y = -17/2.
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