Solve the simultaneous equations: 2x + y = 7x - y = 1.

April 14, 2026Mathematics

ScanSolve AI Answer

April 14, 2026

Answer

$x = \frac{2}{9}, y = \frac{5}{9}$

You're on a roll — Step 1: Separate the given expression into two distinct equations. The problem states $2x + y = 7x - y = 1$ . This can be broken down into: Equation (1): $2x + y = 1$ Equation (2): $7x - y = 1$

Step 2: Add Equation (1) and Equation (2) to eliminate $y$ . $(2x + y) + (7x - y) = 1 + 1$ $2x + 7x + y - y = 2$ $9x = 2$

Step 3: Solve for $x$ . $x = \frac{2}{9}$

Step 4: Substitute the value of $x$ into Equation (1) to solve for $y$ . Using Equation (1): $2x + y = 1$ Substitute $x = \frac{2}{9}$ : $2\left(\frac{2}{9}\right) + y = 1$ $\frac{4}{9} + y = 1$

Step 5: Solve for $y$ . $y = 1 - \frac{4}{9}$ To subtract, find a common denominator: $y = \frac{9}{9} - \frac{4}{9}$ $y = \frac{5}{9}$

The solution to the simultaneous equations is $\boxed{x = \frac{2}{9}, y = \frac{5}{9}}$ .

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You're on a roll — Step 1: Separate the given expression into two distinct equations.

Asked on April 14, 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 14, 2026

You're on a roll — Step 1: Separate the given expression into two distinct equations. The problem states 2x + y = 7x - y = 1. This can be broken down into: Equation (1): 2x + y = 1 Equation (2): 7x - y = 1 Step 2: Add Equation (1) and Equation (2) to eliminate y. (2x + y) + (7x - y) = 1 + 1 2x + 7x + y - y = 2 9x = 2 Step 3: Solve for x. x = (2)/(9) Step 4: Substitute the value of x into Equation (1) to solve for y. Using Equation (1): 2x + y = 1 Substitute x = (2)/(9): 2((2)/(9)) + y = 1 (4)/(9) + y = 1 Step 5: Solve for y. y = 1 - (4)/(9) To subtract, find a common denominator: y = (9)/(9) - (4)/(9) y = (5)/(9) The solution to the simultaneous equations is x = (2)/(9), y = (5)/(9). What's next?

Asked on April 14, 2026Mathematics

ScanSolve AI AnswerAnswered on April 14, 2026

You're on a roll — Step 1: Separate the given expression into two distinct equations. The problem states 2x + y = 7x - y = 1. This can be broken down into: Equation (1): 2x + y = 1 Equation (2): 7x - y = 1 Step 2: Add Equation (1) and Equation (2) to eliminate y. (2x + y) + (7x - y) = 1 + 1 2x + 7x + y - y = 2 9x = 2 Step 3: Solve for x. x = (2)/(9) Step 4: Substitute the value of x into Equation (1) to solve for y. Using Equation (1): 2x + y = 1 Substitute x = (2)/(9): 2((2)/(9)) + y = 1 (4)/(9) + y = 1 Step 5: Solve for y. y = 1 - (4)/(9) To subtract, find a common denominator: y = (9)/(9) - (4)/(9) y = (5)/(9) The solution to the simultaneous equations is x = (2)/(9), y = (5)/(9). What's next?