Solving simultaneous linear equations graphically | Maths

Starter quiz

Using substitution, what is the value of $x$ for simultaneous equations $6x + 4y = 32$ and $x + 3y = 17$ ?

'2' ✓
Using substitution, what is the value of $x$ for simultaneous equations $6x + 4y = 64$ and $x + 3y = 34$ ?

'4' ✓
Using substitution, what is the value of $y$ for simultaneous equations $10x + 8y = 56$ and $x + 3y = 10$ ?

'2' ✓
Using substitution, what is the value of $y$ for simultaneous equations $14x + 4y = 6$ and $2x = 3 - y$ ?

'5' ✓
Using substitution, what is the value of $y$ for simultaneous equations $14x + 4y = 72$ and $2x + y = 15$ ?

'11' ✓
Using substitution, what is the value of $y$ for simultaneous equations $2y - 2x = -2$ and $3x + y = 19$ ?

'4' ✓

If A and B are simultaneous equations such that A: $x + 2y = 21$ and B: $3x + y = 43$ where will coordinate pair $(1, 10)$ go in the Venn diagram?

In A but not B ✓

In B but not A

The intersection of A and B

Outside of both A and B
If A and B are simultaneous equations such that A: $2x + 2y = 10$ and B: $3x + y = 7$ where will coordinate pair $(1, 4)$ go in the Venn diagram?

In A but not B

In B but not A

The intersection of A and B ✓

Outside of both A and B
If A and B are simultaneous equations such that A: $2y - 2x = 8$ and B: $3x + y = 4$ where will coordinate pair $(0, 0)$ go in the Venn diagram?

In A but not B

In B but not A

The intersection of A and B

Outside of both A and B ✓
If A and B are simultaneous equations such that A: $3x + y = 40$ and B: $7x + y = 88$ where will coordinate pair $(12, 4)$ go in the Venn diagram?

In A but not B

In B but not A

The intersection of A and B ✓

Outside of both A and B
If A and B are simultaneous equations such that A: $3x + y = 13$ and B: $7x + 6y = 34$ where will coordinate pair $(5, -2)$ go in the Venn diagram?

In A but not B ✓

In B but not A

The intersection of A and B

Outside of both A and B
If A and B are simultaneous equations such that A: $3x + y = 9$ and B: $4x +3y = 7$ where will coordinate pair $(1, 1)$ go in the Venn diagram?

In A but not B

In B but not A ✓

The intersection of A and B

Outside of both A and B

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You can use your knowledge of linear graphs to draw the graphs of both equations on the same axes.
If there exists a solution, the point of intersection is that solution.
If the lines are parallel then there are no solutions.
If the lines lie on top of each other, there are infinitely many solutions.

Equations always have one solution.

Some equations have one solution but, some have no solutions, some have two solutions, some have more than two solutions.

Linear - The relationship between two variables is linear if, when plotted on a pair of axes, a straight line is formed.