Equations which represent different relationships between the same variables are called simultaneous equations.

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

Checking and securing understanding of simultaneous equations

Maths

In this unit, pupils will learn how to extend their understanding of solving equations and extend this to consider inequalities. Pupils will consider a variety of inequalities and ways that their solutions can be represented.

Inequalities

The __________ shows us a value of $$x$$ and $$y$$ that satisfies two linear equations simultaneously when plotted.

Here are the lines with equations $$y=2x+1$$ and $$y=5-2x$$. What is the solution to both equations simultaneously?

How many solutions are there to the equations $$y=2x+8$$ and $$y=2x+3$$ when solved simultaneously?

How many solutions are there to the equations $$2y=3x+4$$ and $$4y-6x=8$$ when solved simultaneously?

Here is the line with equation $$y=x-1$$. What is the solution to the simultaneous equations $$y=x-1$$ and $$y=2x-4$$?

Here is the line with equation $$y=x-1$$. What is the solution to the simultaneous equations $$y=x-1$$ and $$3y+2x=12$$?

Which of these are solutions to the equation $$y=3x-4$$?

What is the gradient of the line with equation $$y=4x+2$$ ?

What is the gradient of the line with equation $$2y+5x=10$$ ?

What is the $$x$$ intercept of the line with equation $$3y+4x=12$$ ?

Fill in the missing coordinate for the $$y$$ intercept of the line with equation $$3y+4x=12$$ (0, {{}})

Which of these shows the line with equation $$2y=6-4x$$ ?

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