System of Equations Example

Grades 8-9GCSEÅrskurs 9

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

3x + (2x + 1) = 11

Simplify and solve for x

Combine like terms: 5x + 1 = 11. Subtract 1: 5x = 10. Divide by 5: x = 2

x = 2

Find y

Substitute x = 2 into y = 2x + 1: y = 2(2) + 1 = 5

y = 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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