Problem
Solve the system: y = 2x + 1 and 3x + y = 11
📝Step-by-Step Solution
Choose the substitution method
Since y is already isolated in the first equation (y = 2x + 1), we'll substitute this into the second equation.
Substitute
Replace y in the second equation with (2x + 1): 3x + (2x + 1) = 11
Simplify and solve for x
Combine like terms: 5x + 1 = 11. Subtract 1: 5x = 10. Divide by 5: x = 2
Find y
Substitute x = 2 into y = 2x + 1: y = 2(2) + 1 = 5
Check the solution
Check in both equations: y = 2(2) + 1 = 5 ✓ and 3(2) + 5 = 11 ✓
✅Final Answer
x = 2, y = 5 or (2, 5)
The solution (2, 5) is where the two lines intersect on a graph. Systems can have one solution (intersecting lines), no solution (parallel lines), or infinitely many solutions (same line). Elimination is another method that works well when both equations are in standard form.
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