How do you find the value of simultaneous equations?

Download Article

Simultaneous equations are two linear equations with two unknown variables that have the same solution. Solving equations with one unknown variable is a simple matter of isolating the variable; however, this isn’t possible when the equations have two unknown variables. By using the substitution method, you must find the value of one variable in the first equation, and then substitute that variable into the second equation.[1] While it involves several steps, the substitution method for solving simultaneous equations requires only basic algebra skills.

1. 1

   Choose the equation you want to work with first. It doesn’t matter which equation you choose, but you might want to look for one that will give you numbers that are easier to work with.[2]

2. 2

   Isolate the variable in the first equation. You could also start by isolating the y variable (or whatever other variable the equation uses).[3]

   Advertisement

3. 3

   Plug in the value of into the second equation. Place the value in parentheses for clarity.[4]

4. 4

   Find the value of in the second equation. Remember to follow the order of operations.[5]

Advertisement

1. 1

2. 2

   Find the value of . Remember to follow the order of operations.[8]

3. 3

   Check your work. To do this, substitute the values you found for and into both equations, and verify that the resulting equation are true.[9]

Advertisement

Add New Question

• Question

  Is there an easier method for simultaneous equations than what is already on this website?

  Not really. Here's the simplest example possible: let's say x + y = 3 and x - y = 1. Solve the second equation for x by adding y to both sides: (x - y) + y = 1 + y. So x = 1 + y. Take that value of x, and substitute it into the first equation given above (x + y = 3). With that substitution the first equation becomes (1+y) + y = 3. That means 1 + 2y = 3. Subtract 1 from each side: 2y = 2. So y = 1. Substitute that value of y into either of the two original equations, and you'll get x = 2.

• Question

  Is 3x + 4y = 52 and 5x + y = 30 solvable by substitution? I've tried solving twice and I just can't get the last part right.

  Yes, it's solvable. Take the second equation, and subtract 5x from both sides: y = (30 - 5x). Plug that value of y back into the other equation: 3x + 4(30 - 5x) = 52. So (3x + 120 - 20x) = 52, and (-17x + 120) = 52. Then (-17x) = -68, and x = 4. Plug that value of x into either of the original equations: 3(4) + 4y = 52, so 12 + 4y = 52, and 4y = 40, so that y = 10. Check your work by plugging the found values of x and y into either of the original equations.

• Question

  Which is easiest between the elimination, graphical, and substitution methods of solving simultaneous equations?

  It depends on what kind of equation you have. One skill you should develop is knowing when to use what so you can manage your time wisely.

See more answers

Ask a Question

200 characters left

Include your email address to get a message when this question is answered.

Submit

Advertisement

Video

Thanks for submitting a tip for review!

About This Article

Thanks to all authors for creating a page that has been read 176,404 times.

Did this article help you?

How do you solve simultaneous equations with examples?

What are the 3 ways to solve simultaneous equations?