Mentor Teaching · Model and guided practice

Solve a Linear System and Check Both Equations

Worked teaching example

Solve y = x + 2 and x + y = 8 by substitution. Give the ordered pair and check it in both original equations.

Teaching example — reasoning intentionally shown

A system solution makes both equations true for the same pair. Since y equals x + 2, replace y by the whole expression x + 2 in the other equation: x + (x + 2) = 8. Combine to 2x + 2 = 8, subtract 2 to get 2x = 6 and divide by 2 to get x = 3. Then y = 5. Check 5 = 3 + 2 and 3 + 5 = 8 before reporting (3, 5).

Mentor Teaching · Model and guided practice

Solve a Linear System and Check Both Equations

Guided practice 1

Solve y = 2x + 1 and x + y = 10. Show the substitution and check the ordered pair in both equations.

Show or explain your reasoning. Use the space below or continue on separate paper.

Mentor Teaching · Model and guided practice

Solve a Linear System and Check Both Equations

Guided practice 2

A learner proposes (4, 3) for x + y = 7 and 2x - y = 2. Check both equations. Does this pair solve the system? Explain without solving for a new pair.

Show or explain your reasoning. Use the space below or continue on separate paper.

Mentor Teaching · Model and guided practice

Solve a Linear System and Check Both Equations

Guided practice 3

Solve x = y - 1 and 2x + y = 7. Show which expression replaces x and verify both values.

Show or explain your reasoning. Use the space below or continue on separate paper.