Systems of Equations with Two Variables Worksheets
Gain immense practice with this batch of printable solving systems of equations worksheets, designed for 8th grade and high school students. Find adequate exercises to solve a set of simultaneous equations with two variables using the graphing method and algebraic methods like the substitution method, elimination method, cross-multiplication method. Also, find practice PDFs on Cramer's Rule and reciprocal equations. Access some of them for free!
Direct students of high-school to graph both the linear equations on the coordinate plane using the slope-intercept form of the equation. The point where both the lines intersect is the solution to the systems of equations.
Substitution method is the technique of rearranging either of the equations and making one variable the subject. Plug in this value in the other equation to find the ordered pair that makes both equations true.
Instruct grade 8 and high school students to line up the like variables, multiply with a constant to obtain an equivalent linear equation if required and then add or subtract to eliminate one variable and find the value of the other. Substitute its value to find the value of the eliminated variable.
Cross-multiply the coefficients in order to determine the value of the variables. Substitute the coefficients, variables and constants in the cross-multiplication formula and find the solution to the simultaneous pairs of equations.
Cramer's rule is an efficient way to solve systems of equations. Set up a coefficient matrix, an x-matrix and a y-matrix. Compute the determinants of each 2 x 2 matrix. Divide the determinants of the x-matrix and the y-matrix with the coefficient determinant to solve for the two variables.
Each solving the systems of equations pdf worksheet provides eight pairs of simultaneous equations. Apply any method according to your discretion and find the solution to the systems of equations.
This array of printable worksheets comprises systems of linear equations consisting of fractions. Assign the value of each fraction to a variable. Solve for the variables using any method; convert the answers to their reciprocals to find the solution to the simultaneous equations.