4x+y==21
7x-4y=8
4x+5y=5
x=y-10
4x+y=21
7x-4y=8
21*8=168
-------------
8(4x+y)=21(7x-4y)
Solve
John's idea is interesting, but leaves you no closer to the solution.
4x+y=21
7x-4y=8
Consider his multiplication idea, and work it this way:
28x+7y = 147
28x-16y = 32
Now subtract to get
23y = 115
y = 5
now you can find x easily.
The other set is even simpler. You know what x is, so plug it in:
4(y-10)+5y=5
4y-40+5y=5
9y=45
y=5
Now get x
To find the solution to this system of equations, you can use a method called "substitution" or "elimination." I'll explain how to use the substitution method.
The given system of equations is:
1) 4x + y = 21
2) 7x - 4y = 8
Step 1: Solve one of the equations for one variable in terms of the other variable. Let's solve equation 1) for y:
4x + y = 21
Subtract 4x from both sides:
y = 21 - 4x
Step 2: Substitute the expression of y from step 1) into equation 2) to eliminate the variable y:
7x - 4(21 - 4x) = 8
Simplify and solve for x:
7x - 84 + 16x = 8
Combine like terms:
23x - 84 = 8
Add 84 to both sides:
23x = 92
Divide both sides by 23:
x = 4
Step 3: Substitute the value of x back into equation 1) to find the value of y:
4(4) + y = 21
16 + y = 21
Subtract 16 from both sides:
y = 5
Therefore, the solution to the system of equations is x = 4 and y = 5.