A math test on solving systems of two equations with two unknowns.
This proctored assignment in ninth grade (3ème) is for teachers and students who want to review a test
math on systems of two equations with the substitution method or the addition method (linear combination). To use the substitution method, one of the unknowns must be isolated in one of the equations. Then, replace the isolated unknown by its value in the second equation. Then, we need to isolate the remaining unknown. Finally, you will replace this unknown by its exact value in the remaining equation.
It is possible to solve this system with the combination method. This method is based on two principles. First, we can multiply any equation in the system by a constant and we will have an equivalent system. Then, we can replace one equation of the system by its sum with any equation of the system and we will also have an equivalent system.
Thus, any equation of the first degree with two unknowns has exactly one infinity of solutions. Indeed, its graphical representation is a line with an infinity of points with coordinates that are solutions of this equation. Therefore, if we consider a system of two equations with two unknowns, its solutions will be the pairs of real numbers (x, y) which must verify both the first and the second equation.
Exercise 1: (6 points)
Solve the following systems:
Exercise n° 2 : (extract from the brevet Métropole) (4 points)
For 6 kilograms of varnish and 4 liters of wax, we pay 95 euros.
For 3 kilograms of varnish and 3 liters of wax, we pay 55.50 euros.
What is the price per kilogram of varnish and per liter of wax?
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