algebra · worked example

Solve system: 2x+y=7 and x-y=2

Method: elimination. Verified step-by-step solution with our free AI math solver.
Problem

{2x+y=7x−y=2\begin{cases} 2x + y = 7 \\ x - y = 2 \end{cases}

Step-by-step solution

  1. Add the two equations to eliminate yy: (2x+y)+(x−y)=7+2(2x + y) + (x - y) = 7 + 2, so 3x=93x = 9.

  2. Solve for xx: x=3x = 3.

  3. Substitute back into either equation. Using the second: 3−y=23 - y = 2, so y=1y = 1.

  4. Verify in the first: 2(3)+1=72(3) + 1 = 7. ✓

Answer

(x,y)=(3,1)(x, y) = (3, 1)

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