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Simple Simultaneous Equations

Solve using Trial & Error

One method which we can use to solve any type of equation is the rial and error method. We can look at the equation and try out different combinations of numbers and see if they work. You can do the same with simultaneous equations. If you find the two unknown and they work for both equations, you have solved them. When using trial and error, start of by replacing the letters with two numbers that seem logical to you. If the answer is not correct, use your maths skills to modify the number(s) accordingly so that you get closer and closer to making the equation work. You must remember though that the values have to work in both equations. However, you should try not to use trial and error as it is not very mathematical and very time consuming. Furthermore, if you work with equations where the unknown is not a whole number, it will take a lot of time to find the correct decimal. This is why you should rather use one of the other two methods to solve simultaneous equations.
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Solve using Substitution

We can solve simultaneous equations by substituting one equation into the other so that we only have one equation with one unknown to work with. The same has been done in the example with equation (1) and (2). We have substituted equation (1) into equation (2) by replacing the y in (2) by 4x+3 from (1). Then we have solved it like a linear equation. We have then substituted the value of x which we have found into equation (1). We only had to simplify the equation to find the value of y. When you do simultaneous equations, you should always check that your values are correct by substituting them into one of the equations.
Example 1 We have solved the simultaneous equation by substituting equation (1) into equation (2) and then solving the linear equation. After that we have substituted the value of y into equation (1) and then solved it. We ended up with our two values of x (-3) and y (-3).
Example 2 We have solved the simultaneous equation by substituting equation (2) into equation (1) and then solving the linear equation. We have then substituted the value of x into equation (2) and then solved it to find the value of y. x=2 and y=3.

Solve using Elimination

The elimination method involves subtracting or adding the equations to eliminate one of the unknowns. We first have to make sure that both equations have the same number of one of the unknowns. In the example, we multiplied equation (1) by 3 and equation (2) by 2 to have 12y in both equations. Then we have subtracted equation (1) from equation (2) which gave us x=3. The last step is to substitute x=3 into equation (1) and solve it to find the value of y. Check your answer at the end.
Example 1 We have solved the simultaneous equation by eliminating the x in both equations. This was achieved by multiplying equation (1) by 2 and then subtracting equation (2) from it. This allowed us to find the value of y. We then substituted the value of y into equation (1) and solved it to fin the value of x. x=6 and y=1.
Example 2 We have solved the simultaneous equation by eliminating the x in both equations. This was achieved by adding equation (2) to equation (1) which enabled us to find the value of y. we have then substituted the value of y into equation (1) and solved it to find the value of x. x=2 and y=3.

Moving on to Advanced Simultaneous Equations

Try to do simultaneous equations with one linear and one quadratic next.  Please share this page if you like it or found it helpful!
Solving Simultaneous Equations With One Linear & One Quadratic
16.0 SIMULTANEOUS EQUATIONS 16.2 SIMULTANEOUS EQUATIONS WITH ONE LINEAR AND ONE QUADRATIC
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Chapter 16.1:  Learning Outcomes Students will learn how to solve simple simultaneous equations using trial and error! Students will learn how to solve simple simultaneous equations using elimination! Students will learn how to solve simple simultaneous equations using substitution!

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