Step 1: Label the given equations. 2x − y = 3 (1); x + y = 9 (2) Step 2: Add equation (1) and equation (2) to eliminate y. Formula: (2x − y) + (x + y) = 3 + 9; Substitute: 2x + x − y + y = 12; Simplify: 3x = 12 Step 3: Solve for x. x = 12/3; x = 4; Step 4: Substitute x = 4 into equation (2). Formula: x + y = 9; Substitute: 4 + y = 9; Simplify: y = 9 − 4; y = 5 Step 5: Verify the solution in equation (1). Substitute x = 4 and y = 5: 2(4) − 5 = 8 − 5; 8 − 5 = 3 The solution checks out. Final answer: x = 4 , y = 5; x=4, y=5

2x−y=3. X+y=9

March 19, 2026Mathematics

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Answer

x=4,\ y=5

Step-by-step solution

5 steps

Label the given equations.
$2x - y = 3 \quad (1)$ $x + y = 9 \quad (2)$
Add equation (1) and equation (2) to eliminate y.
Formula: $(2x - y) + (x + y) = 3 + 9$

Substitute: $2x + x - y + y = 12$

Simplify: $3x = 12$
Solve for x.
$x = \frac{12}{3}$ $x = 4$
Substitute x = 4 into equation (2).
Formula: $x + y = 9$

Substitute: $4 + y = 9$

Simplify: $y = 9 - 4$
$y = 5$
Verify the solution in equation (1).
Substitute x = 4 and y = 5: $2(4) - 5 = 8 - 5$
$8 - 5 = 3$
The solution checks out.

Final answer: $x = 4$ , $y = 5$

x=4,\ y=5

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2x−y=3. X+y=9

Answer

Step-by-step solution

Label the given equations.

Add equation (1) and equation (2) to eliminate y.

Solve for x.

Substitute x = 4 into equation (2).

Verify the solution in equation (1).

Try one yourself

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