Solve the simultaneous equations
1 answer:
Answer:
The solution for given system of equations is: x = 6 and y = 3
Or
(6,3)
Step-by-step explanation:
Given equations are:
There are three methods to solve simultaneous equations
- Elimination
- Substitution
- Co-efficient method
We will use the elimination method as the coefficients of x in both equations are already same
Subtracting equation 2 from equation 1
Putting y = 3 in equation 2
Hence,
The solution for given system of equations is: x = 6 and y = 3
Or
(6,3)
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1- Solution using graphs:
Take a look at the attached images.
The red graph represents the first given function while the blue graph represents the second given function.
We can note that the two graphs are the same line (they overlap).
This means that any chosen point on one of them will satisfy the other.
This means that there are infinite number of solutions to these two equations.
2- Solution using substitution:
The first given equation is:
y = -5x + 3 ...........> equation I
The second given equation is:
2y + 10x = 6 ...........> equation II
Substitute with I in II and solve as follows:
2(-5x+3) + 10x = 6
-10x + 6 + 10x = 6
0 = 0
This means that there are infinitely many solutions to the given system of equations.
Hope this helps :)
Take a look at the attached images.
The red graph represents the first given function while the blue graph represents the second given function.
We can note that the two graphs are the same line (they overlap).
This means that any chosen point on one of them will satisfy the other.
This means that there are infinite number of solutions to these two equations.
2- Solution using substitution:
The first given equation is:
y = -5x + 3 ...........> equation I
The second given equation is:
2y + 10x = 6 ...........> equation II
Substitute with I in II and solve as follows:
2(-5x+3) + 10x = 6
-10x + 6 + 10x = 6
0 = 0
This means that there are infinitely many solutions to the given system of equations.
Hope this helps :)