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Solving Linear Simultaneous Equations - Same Coefficients WORKSHEET

Suitable for Grades: Algebra I, IM 1

CCSS: HSA.REI.C.5, HSA.REI.C.7

CCSS Description: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x2 + y2 = 3.

Solving Linear Simultaneous Equations - Same Coefficients WORKSHEET DESCRIPTION

Let your students focus on which variable to eliminate and how with this worksheet that consists of pairs of linear simultaneous equations where one coefficient is the same in both equations.

Section A acts as a warm up as students use substitution to check whether given values are the correct solutions to five pairs of equations.

In Section B, learners will decide which variable should be eliminated and whether addition or subtraction should be used in order to eliminate it in a further five pairs of equations.

Students will solve 8 systems of simultaneous equations in Section C. All solutions are integers and most are positive.

Lastly, Section D asks students to form and solve a pair of simultaneous equations in order to solve a worded problem.