Solve the system of linear equations: 3x - 2y = 19 and 5x + 2y = 21.

April 16, 2026Mathematics

ScanSolve AI Answer

April 16, 2026

Answer

x=5, y=-2

Here are the given equations: $3x - 2y = 19 \quad (1)$ $5x + 2y = 21 \quad (2)$

Step 1: Add equation (1) and equation (2) to eliminate $y$ . $(3x - 2y) + (5x + 2y) = 19 + 21$ $3x + 5x - 2y + 2y = 40$ $8x = 40$

Step 2: Solve for $x$ . $\frac{8x}{8} = \frac{40}{8}$ $x = 5$

Step 3: Substitute the value of $x = 5$ into equation (1). $3(5) - 2y = 19$ $15 - 2y = 19$

Step 4: Solve for $y$ . $-2y = 19 - 15$ $-2y = 4$ $\frac{-2y}{-2} = \frac{4}{-2}$ $y = -2$

The solution is $x=5$ and $y=-2$ . $\boxed{x=5, y=-2}$ 3 done, 2 left today. You're making progress.

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3x - 2y = 19 (1) 5x + 2y = 21 (2) Step 1: Add equation (1) and equation (2) to eliminate y.

Asked on April 16, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 16, 2026

Here are the given equations: 3x - 2y = 19 (1) 5x + 2y = 21 (2) Step 1: Add equation (1) and equation (2) to eliminate y. (3x - 2y) + (5x + 2y) = 19 + 21 3x + 5x - 2y + 2y = 40 8x = 40 Step 2: Solve for x. (8x)/(8) = (40)/(8) x = 5 Step 3: Substitute the value of x = 5 into equation (1). 3(5) - 2y = 19 15 - 2y = 19 Step 4: Solve for y. -2y = 19 - 15 -2y = 4 (-2y)/(-2) = (4)/(-2) y = -2 The solution is x=5 and y=-2. x=5, y=-2 3 done, 2 left today. You're making progress.