Exam-Style Problems

Stage 9 - Q1 - 2 marks

19277

Read the simultaneous solution from the graph and verify it.

\[y=2 x + 4\]

\[y=12 - 2 x\]

x

y

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12

\(y=2 x + 4\)

\(y=12 - 2 x\)

Hint

Read \(x\) first, then \(y\) at the intersection.

Stage 9 - Q2 - 2 marks

19278

Draw both lines on the grid using at least two points each. Read their intersection and check algebraically.

\[y=2 x\]

\[y=16 - 2 x\]

x

y

0

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12

Hint

Useful plotting inputs lie one unit either side of the intersection; choose any two points visible on the grid.

Stage 9 - Q3 - 3 marks

19279

Read the simultaneous solution from the graph and verify it.

\[y=x + 3\]

\[y=21 - 2 x\]

x

y

0

2

4

6

8

3

6

9

12

\(y=x + 3\)

\(y=21 - 2 x\)

Hint

Read \(x\) first, then \(y\) at the intersection.

Stage 9 - Q4 - 3 marks

19280

Draw both lines on the grid using at least two points each. Read their intersection and check algebraically.

\[y=2 x + 3\]

\[y=12 - x\]

x

y

0

2

4

6

8

3

6

9

12

Hint

Useful plotting inputs lie one unit either side of the intersection; choose any two points visible on the grid.

Stage 9 - Q5 - 4 marks

19281

Two algebraic models are shown. At which input do they give the same output? State that output.

\[y=2 x - 7\]

\[y=8 - x\]

x

y

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12

\(y=2 x - 7\)

\(y=8 - x\)

Hint

Use the intersection, not either intercept.

Stage 9 - Q6 - 4 marks

19282

Two algebraic models are shown. At which input do they give the same output? State that output.

\[y=x + 1\]

\[y=7 - 2 x\]

x

y

0

2

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6

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9

12

\(y=x + 1\)

\(y=7 - 2 x\)

Hint

Use the intersection, not either intercept.

Stage 9 - Q7 - 5 marks

19283

A learner proposes \(P=(5,6)\) as the simultaneous solution. Use the graph and substitution to assess it.

\[y=2 x - 4\]

\[y=12 - 2 x\]

x

y

0

2

4

6

8

3

6

9

12

\(y=2 x - 4\)

\(y=12 - 2 x\)

Hint

A point must lie on both graphs to be a simultaneous solution.

Stage 9 - Q8 - 5 marks

19284

Explain why this system has no simultaneous solution.

\[y=x+5\]

\[y=x+9\]

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\(y=x + 5\)

\(y=x + 9\)

Hint

Compare the common gradient and different intercepts.

Stage 9 - Q9 - 5 marks

19285

Explain how many simultaneous solutions this system has.

\[y=x+3\]

\[2y=2x+6\]

x

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\(y=x + 3\)

Hint

Simplify one equation before comparing the graphs.

Stage 9 - Q10 - 3 marks

19286

Use the graph to solve the first two equations. A third line \(y=kx-2\) passes through the same intersection. Find \(k\) and verify all three equations.

\[y=2x+1\]

\[y=-x+10\]

x

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\(y=2 x + 1\)

\(y=10 - x\)

Hint

The same coordinates must satisfy the third equation.