Solving Simultaneous Equations Graphically worksheet
5 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.
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2 marks
The graphs of \(y = -x + 7\) and \(y = x + 1\) cross at the point \((3, 4)\).
(a)Write down the solution of the simultaneous equations
\(y = -x + 7\)
\(y = x + 1\)
(b)The graph of \(y = -3x + 13\) also passes through \((3, 4)\).
Write down the solution of the simultaneous equations
\(y = -x + 7\)
\(y = -3x + 13\)
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3 marks
Omar is solving the simultaneous equations
\(y = -x - 4\)
\(y = 2x - 7\)
by drawing both graphs. Omar says the graphs cross at \((1, -5)\).
(a)Calculate the value of \(y\) given by \(y = -x - 4\) when \(x = 1\).
(b)Calculate the value of \(y\) given by \(y = 2x - 7\) when \(x = 1\).
(c)Is his answer right? Give a reason.
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3 marks
The graph of \(y = 2x + 8\) is drawn on the grid below.
By drawing the graph of \(y = -x + 2\) on the same grid, solve the simultaneous equations
\(y = 2x + 8\)
\(y = -x + 2\)
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2 marks
The graphs of \(y = -x - 1\) and \(y = x - 7\) cross at the point \((3, -4)\).
(a)Write down the solution of the simultaneous equations
\(y = -x - 1\)
\(y = x - 7\)
(b)The graph of \(y = 3x - 13\) also passes through \((3, -4)\).
Write down the solution of the simultaneous equations
\(y = -x - 1\)
\(y = 3x - 13\)
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3 marks
Leila is solving the simultaneous equations
\(y = 2x - 11\)
\(y = -3x + 9\)
by drawing both graphs. Leila says the graphs cross at \((4, -3)\).
(a)Work out the value of \(y\) given by \(y = 2x - 11\) when \(x = 4\).
(b)Work out the value of \(y\) given by \(y = -3x + 9\) when \(x = 4\).
(c)Is her answer right? Give a reason.
Answers
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(a) \(x = 3\), \(y = 4\)
(b) \(x = 3\), \(y = 4\) -
(a) \(-5\)
(b) \(-5\)
(c) Yes — the point is on both graphs - \(x = -2\), \(y = 4\)
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(a) \(x = 3\), \(y = -4\)
(b) \(x = 3\), \(y = -4\) -
(a) \(-3\)
(b) \(-3\)
(c) Yes — the point is on both graphs