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We saw several methods to use substitution to solve systems of equations. Remember the goal is to find the x & y value that "works" for both equations .... (x, y)

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We saw several methods to use substitution to solve systems of equations. Remember the goal is to find the x & y value that "works" for both equations .... (x, y)

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Today we graphed systems of equations in the form Ax+By=C....meaning they were not in slope intercept form. We used either desmos or geogebra to graph them.

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Today we graphed systems of equations in the form Ax+By=C....meaning they were not in slope intercept form. We used either desmos or geogebra to graph them.

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Systems of equations have solutions of x and y coordinates that work in both equations if you substitute the values into them

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Systems of equations have solutions of x and y coordinates that work in both equations if you substitute the values into them

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Just like last year, you saw that you can graph two equations and the solution is the point where the two lines cross

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Just like last year, you saw that you can graph two equations and the solution is the point where the two lines cross

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If you put in y=0 then solve for y, you get the x-intercept (x,0)

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If you put in y=0 then solve for y, you get the x-intercept (x,0)

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If you put in x=0 then solve for y, you get the y-intercept (0,y)

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If you put in x=0 then solve for y, you get the y-intercept (0,y)

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We saw equations in the form Ax + By = C and used them to find x & y intercepts and slopes

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We saw equations in the form Ax + By = C and used them to find x & y intercepts and slopes

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We reviewed the properties of equality that allow us to rearrange, simplify, and rebalance an equation 

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We reviewed the properties of equality that allow us to rearrange, simplify, and rebalance an equation 

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We saw a variety of ways to rearrange equations to solve them for a variable. 

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We saw a variety of ways to rearrange equations to solve them for a variable. 

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This can be useful if you repeatedly have to input a value and solve the equation for other variables over and over and over again.

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Solve and Rearrange Multi-Variable Equations - Sheaff Math

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We learned how you can create an infinite number of equivalent equations for a situation.                    Some will be more useful like turning decimals to whole numbers; some will be more simplified and will be easier to solve; some will tell the story better but will have more parts to them.  

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We learned how you can create an infinite number of equivalent equations for a situation.                    Some will be more useful like turning decimals to whole numbers; some will be more simplified and will be easier to solve; some will tell the story better but will have more parts to them.  

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We used graphing calcs/app to graph linear equations and identify solutions to the equations

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We used graphing calcs/app to graph linear equations and identify solutions to the equations

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We tried to understand how the coordinates of the points on the graph of an equation are related to the equation.

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We tried to understand how the coordinates of the points on the graph of an equation are related to the equation.

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We were given the graph of a linear equation, we tried to explain the meaning of the points on the graph to explain the situation it represents.

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We were given the graph of a linear equation, we tried to explain the meaning of the points on the graph to explain the situation it represents.

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All math models are simplifications of the real-world. They put constraints and help us focus on a limited area of the problem

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All math models are simplifications of the real-world. They put constraints and help us focus on a limited area of the problem

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this can be good and bad

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Models in Math are equations, graphs and other math tools used to represent a situation & PREDICT the past, present or , Future. 

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Models in Math are equations, graphs and other math tools used to represent a situation & PREDICT the past, present or , Future. 

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The key word is that Algebra helps us make PREDICTIONS.

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It's important to be able to read an equation and "tell a story" about it. 

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It's important to be able to read an equation and "tell a story" about it. 

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For example the equation
T + 50 = .5n
Could mean that if everyone in the club donates 50 cents, then they will have raised $50 more than their fundraising goal for the Senior Citizens Center

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We learned that it's important to be able to take real-world situations and write expressions and equations that represent and FIT those situations

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We learned that it's important to be able to take real-world situations and write expressions and equations that represent and FIT those situations

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GCSE Maths - How to Rearrange Formulas (2026/27 exams)