While if Bob gave Andre 22, Andre would then have twice as much as Bob.Therefore there must be two equations.In general, the number of equations must equal the number of unknowns.) How can we get two equations out of the given information We must translate each verbal sentence into the language of algebra.
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The final solution, then, will have 9 gallons of pure alcohol. How much water must you add to how much saline solution, in order to dilute it to 8 gallons of 15 solution. So the question is, What is s so that 20 of s -- the salt -- will be 15 of 8 gallons. We saw there that speed, or velocity, is distance divided by time. We provide high-quality math worksheets for more than 10 million teachers and homeschoolers every year. Worksheets Click below for the Simultaneous Equations Worksheet Generator which provides limitless questions for practice. ![]() Solving Graphically For each equation, find coordinates for two points on the graph. An easy way of doing this is finding corresponding values when x 0 and when y 0. 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.) For 4x 2y 10 this gives (2.5, 0) and (0,-5) which we plot and then extend a straight line through. For x y 4 this gives (0,4) and (4,0) which we plot and then extend a straight line through. Notice that the all the coordinates through which the lines pass are solutions to each equation. And the coordinates of the point at which they cross, (3,1)is the solution to the pair of simultaneous equations. Solving Algebraically We can find solutions to simultaneous equations algebraically too. Which one you choose might depend on the values involved or it might just be the method you like the most. Elimination Method 4x 2y 10 x y 4 Multiply x y 4 by 2 to give 2x 2y 8 4x 2y 10 2x 2y 8 6x 18 x 3 We then add the two equations which eliminates the 2y (since -2y 2y 0) and leaves 6x 18 which, after dividing both sides by 6 leaves x 3 3 y 4 y 1 We can then replace x in one of the equations with the value 3. It is always a good idea to check the values for x and y in the other equation. Substitution Method 4x 2y 10 x y 4 Rearrange one equation to get make either x or y subject of the equation. In this case it will be simpler to rearrange x y 4 which we can rearrange to y 4 -x by subtracting x from each side 4x 2y 10 4x 2(4 x) 10 4x 8 2x 10 6x 8 (8) 10 (8) 6x 18 x 3 We then substitute 4 x for y in the other equation. As with the elimination method we then replace x in one of the equations with the value 3. And, as a check, try the values for x and y in the other equation. ![]() Elimination Method 5x 3y 16 4x 5y 5 With this pair of equations we will need to multiply both to get a common multiple of either x or y. We will multiply the top equation by 5 and the bottom one by 3 25x 15y 80 12x -15y 15 13x 65 x 5 We then subtract the two equations which eliminates the -15y and leaves 13x 65 which, after dividing both sides by 13 leaves x 5 (5 x 5) 3y 16 25 3y 16 -3y 16 25 -3y -9 y 3 We then replace x in the top equations with the value 5 to find y. Finally, check the values for x and y in the other equation. Substitution Method 3x 4y 5 x 5y 9 Rearrange one equation to get make either x or y subject of the equation. In this case it will be simpler to rearrange x 5y 9 which we can rearrange to x 9 5y by subtracting 5y from each side 3x 4y 5 3(9 5y) 4y 5 27 15y 4y 5 27 11y 5 -11y 5 27 -11y -22 y 2 We then substitute 9 5y for x in the other equation and solve for y. Simultaneous Equations in Real-life Sam and Jack have 50 between them and Sam has 5 more than Jack. How much money does each have s j 50 s j 5 s 27.50, j 22.50 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. And finally, Remember to practice with questions from the Simultaneous Equations Worksheet Generator. Simultaneous Equation Word Problem Free Math WorksheetsFree Math Worksheets Download 100 free math worksheets and save yourself hours in lesson planning. Each week, we add new math worksheets to the site covering all K-8 topics. Simultaneous Equation Word Problem Download Our CommonClick below to download our Common Core-aligned free samples now. 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