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