Non-solutions to simultaneous linear equations | Maths

Starter quiz

Match up the inequalities to the statements.

$x<3$

⇔

values less than 3 ✓

$x\le3$

⇔

values less than or equal to 3 ✓

$x>3$

⇔

values greater than 3 ✓

$x\ge3$

⇔

values greater than or equal to 3 ✓
Which of these are valid inequalities?

$3<5$ ✓

$2<-2$

$-2>-1$

$-5<-3$ ✓

$-4>0$
Which of these solutions satisfy the equation $y=3x-1$ ?

$x=-3 , y=-8$

$x=0 , y=2$

$x=2 , y=5$ ✓

$x=5 , y=10$

$x=8 , y=21$
Which of these coordinates are on the line with equation $y=2x+5$ ?

(-5, -15)

(-3, -1) ✓

(0, 2)

(4, 28)

(7, 19) ✓
Using the graph or otherwise, what is the solution to the equations $y=2x+5$ and $y=2-x$ simultaneously?

$x=-2, y=4$

$x=-1, y=3$ ✓

$x=0, y=5$

$x=1, y=3$

$x=2, y=0$
Which of these equations is $x=5, y=3$ a solution to?

$y=13-2x$ ✓

$y=x+2$

$y=2x+7$

$y=3x-6$

$y=4x-17$ ✓

Which of these coordinates satisfy the inequality $y>2x$ ?

(0, 3) ✓

(1, 1)

(2, 5) ✓

(3, 4)

(6, 10)
Using the graph of $y=5-2x$ (or otherwise) which coordinates satisfy the inequality $y<5-2x$ ?

(-2, 3) ✓

(0, 6)

(1, 2) ✓

(2, 3)

(3, 0)
Match the solutions to the descriptions. Use the graphs to help you.

$x=-2, y=2$

⇔

Solution to $y=\frac{1}{2}x+3$ but not a solution to $y=3x-2$ ✓

$x=1, y=1$

⇔

Solution to $y=3x-2$ but not a solution to $y=\frac{1}{2}x+3$ ✓

$x=2, y=4$

⇔

Solution to both $y=3x-2$ and $y=\frac{1}{2}x+3$ simultaneously ✓

$x=5, y=5$

⇔

Not a solution to $y=3x-2$ nor a solution to $y=\frac{1}{2}x+3$ ✓
Which statements are true for the point (2, 3)?

$y<2x+1$ ✓

$y>2x+1$

$y<5-2x$

$y>5-2x$ ✓
Match the coordinates to the correct statements.

(-3, 3)

⇔

$y>2x+5$ and $y<2-x$ ✓

(-2, 4)

⇔

$y>2x+5$ and $y=2-x$ ✓

(-1, 2)

⇔

$y<2x+5$ and $y<2-x$ ✓

(0, 5)

⇔

$y=2x+5$ and $y>2-x$ ✓

(1, 1)

⇔

$y<2x+5$ and $y=2-x$ ✓

(2, 2)

⇔

$y<2x+5$ and $y>2-x$ ✓
Which coordinate pair satisfies the inequalities $y>x-1$ and $y<2x-1$ ?

(-2, 2)

(0, 3)

(2, 6)

(3, 4) ✓

(4, 1)

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If a point on neither line is substituted into the equations, neither equation will be valid
If a point on one of the lines is substituted into the equations, one equation will be valid
Depending on the location of the point, the equation may evaluate to a bigger or smaller value
Replacing the equals sign with an inequality sign would make the statement true

Pupils may mix-up the x and y coordinates.

Remind pupils that the x value is read from the x-axis and is read first. The y value is read from the y-axis and is read second.

Simultaneous equations - Equations which represent different relationships between the same variables are called simultaneous equations.
Inequality - An inequality is used to show that one expression may not be equal to another.