Solve the equation system exactly.
21x + 6y = 7
7x + 3y = 3
What does it mean equation system? It gives two formulas so I'm not sure. (Sorry this is typically in swedish and it's called 'ekvationssystemet' so I'm unsure for this one) Is it about the substitution method or something more?
who's to say?
Does x = 1/7 and y = 2/3 work in both equations?
21x + 6y = 7
7x + 3y = 3
21(1/7) + 6(2/3) = 3+4 = 7
7(1/7) + 3(2/3) = 1+2 = 3
So, it looks correct.
An equation system, also known as a system of equations, is a set of two or more equations that need to be solved simultaneously. In this case, you have two equations:
21x + 6y = 7 ---- Equation (1)
7x + 3y = 3 ---- Equation (2)
To solve this system of equations exactly, you can either use substitution or the elimination method. Let's use the elimination method in this case:
1. Multiply Equation (2) by 2 to make the coefficients of 'x' in both equations the same:
2(7x + 3y) = 2(3)
14x + 6y = 6 ---- Equation (3)
2. Now, subtract Equation (3) from Equation (1) to eliminate 'y' and solve for 'x':
(21x + 6y) - (14x + 6y) = 7 - 6
21x - 14x + 6y - 6y = 1
7x + 0 = 1
7x = 1
x = 1/7
3. Substitute the value of 'x' (1/7) into either of the original equations. Let's use Equation (2):
7(1/7) + 3y = 3
1 + 3y = 3
3y = 3 - 1
3y = 2
y = 2/3
So, the solution to the equation system is x = 1/7 and y = 2/3.
21x+6y=7
1(21x+6y)=1*7
21x+6y=7
7x+3y=3
-3(7x+3y)=-3*3
-21x-9y=-9
Then
21x+6y-21x-9y=-9+7
-3y=-2
y=-2/-3
y=2/3
and for X
21x+6y=7
21x+6(2/3)=7
21x+4=7
21x=3
x=3/21
x=1/7
Does that seem correct?