Remember to practice with questions from the Simultaneous Equations Worksheet Generator. This example is quite simple – you might be able to work it out by trial-and-error – but you can use any of the methods above to solve it. Sam and Jack have $50 between them and Sam has $5 more than Jack. Elimination Method Substitution Method Simultaneous Equations in Real-life There is one example of each the elimination and substitution methods for solving simultaneous equations shown below. In x + y =4 is simpler than in 4x – 2y = 10)Īnd, as a check, try the values for x and y in the other equation. We then substitute 4 – x for y in the other equation.Īs with the elimination method we then replace x in one Rearrange x + y = 4 which we can rearrange to y = 4 -x Rearrange one equation to get make either x or y It is always a good idea to check the values for x and y in the other equation. (in this example, doing this in x + y =4 is simpler than in 4x – 2y = 10) We can then replace x in one of the equations with the value 3. We then add the two equations which “eliminates” the 2yĪnd leaves 6x = 18 which, after dividing both sides by 6 leaves x = 3 Multiply x + y = 4 by 2 to give 2x + 2y = 8 We will use the same pair of equations as above. Which one you choose might depend on the values involved or it might just be the method you like the most. We can find solutions to simultaneous equations algebraically too.
And the coordinates of the point at which they cross, (3,1)is the solution to the pair of simultaneous equations. Notice that the all the coordinates through which the lines pass are solutions to each equation. (Note: this will give 2 sets of coordinates which, since the equation is linear, is enough although it is a god idea to check at least one more point on the line.)įor 4x – 2y = 10 this gives (2.5, 0) and (0,-5) which we plot and then extend a straight line through.įor x + y = 4 this gives (0,4) and (4,0) which we plot and then extend a straight line through. An easy way of doing this is finding corresponding values when x = 0 and when y = 0. Solving Graphicallyįor each equation, find coordinates for two points on the graph. In simple terms, the solution to a pair of simultaneous equations is the x and y values of the coordinates of the point at which the graphs cross or intersect. WorksheetsĬlick below for the Simultaneous Equations Worksheet Generator which provides limitless questions for practice. Simultaneous equations are two equations, each with the same two unknowns and are “simultaneous” because they are solved together.