# Thread: Simultaneous Equations

1. ## Simultaneous Equations

Solve the simultaneous equations using the substitution method.
(a) 2x+3y= 22
3x+2y= 28

(b) 3x-2y= 28
4x+5y= -1

Thanks

2x+3y= 22------ 1
3x+2y= 28------ 2
We will do elimination by equating coefficient:
In this we multiply either 1 or both the equations by suitable numbers to ensure that the coefficient of one variably is equal.
In this case we will multiply equation 1 by 3 and 2 by 2 to eliminate x. We get
6x+9y= 66------- 3
6x+4y= 56----- 4
Subtract equation 4 from 3 we get
5y = 10 that gives y = 2, plug this value in any equation 1 or 2.
Let us plug the value in equation 1 we get
2x + 3 x 2 = 22
2x = 22 – 6 = 16
X = 8
Thus the solution is x = 8 y = 2.

We can also solve the equations by elimination by actual substitution:
Let us take the second set of equations:
3x-2y= 28 ---- [1] from this equation we have 3x= 28+2y OR x = (28+2y)/3
Plug in this value for x in other equation i.e., 4x+5y= -1----[2] , we will get:

4 x (28+2y)/3 +5y = -1 Multiplying by 3 we get:
112 + 8y + 15y = -3
23y = -115 that gives y = -5 Plugging this value in any equation ( say equation 1 we get:
3x-2(-5)= 28 OR 3x +10 = 28 that gives x = 6
Thus the solution is x = 6, y = -5

Hi Jasmine

The aim when solving simultaneous equations, using the substitution method is to change one of the equations into the form of x= or y=. When you've done this, you can start the substitution process.
I'll go through the first example:
2x + 3y = 22, 3x + 2y = 28
Step 1 is to change either equation into the form of x= or y=.
If we look at the first equation:
2x + 3y = 22, so:
2x = 22 - 3y, so:
x = 11 - 1.5y (now you have one of the equations in the form of x=.)
Step 2 is to substitute the rearranged equation into the other equation.
3x + 2y = 28, you know that x = 11 - 1.5y, so substitute that into the equation. This will give you:
3(11 - 1.5y) + 2y = 28
Step 3 is to simplify, this gives you:
33 - 4.5y + 2y = 28
33 - 2.5y = 28
2.5y = 5
y = 2
Step 4 is to substitute your y value into the 'x=' equation, to get your value for x.
x = 11 - 1.5y , so:
x = 11 - 1.5(2)
x = 8
Solutions:
y = 2, x = 8

Now that i've given you the steps to solving simultaneous equations using substitution, you should be able to do part b) independently
Hope this helped! I've also made a video on the substitution method if you need more help

The real question is, what kind of help do you need? You say you need to use the "substitution method" to solve the equations. Do you know what "substitution method" means? What kind of algebra courses have you taken?

5. ## Re: Simultaneous Equations

This video should give you a better understanding of how to use the substitution method to solve. ProgressMap - Solving Linear Systems by Substitution - YouTube