Substitution
x - 5y=10
2x - 10y=20
to do substitution: you choose one equation, then represent one of the variables in terms in terms of the other. and finally substitute it the the other equation.
(1) x - 5y = 10
(2) 2x - 10y = 20
here, let's choose equation (1), and let's represent x in terms of variable y:
x - 5y = 10
x = 5y + 10
then we substitute this to equation (2):
2x - 10y = 20
2(5y + 10) - 10y = 20
10y + 20 - 10y = 20
20 = 20
note that when you come with this answer (constant = constant), this means that the lines are coinciding, meaning any point can be a solution, because the equations are "equal". if you observe equation (2), we can factor out 2:
2x - 10y = 20
2(x - 5y) = 2(10)
x - 5y = 10
it becomes equation (1).
hope this helps~ :)
The equations are the same (divide the second equation by 2). There is no solution.
X+4y=8
2x-5y=29
THANK SOOOOO MUCH!!!
5x+5y=16 10x-10y=20
To solve this system of equations using the substitution method, we need to isolate one of the variables in one of the equations and substitute it into the other equation. Let's solve this step-by-step:
Step 1: Solve the first equation for x:
x - 5y = 10
Add 5y to both sides:
x = 5y + 10
Step 2: Substitute the expression for x in the second equation:
2x - 10y = 20
Replace x with (5y + 10):
2(5y + 10) - 10y = 20
Distribute the 2:
10y + 20 - 10y = 20
Simplify:
20 = 20
The equation 20 = 20 is a true statement. This means that the two equations are actually the same line, and therefore have infinitely many solutions.
In summary, the given system of equations has infinitely many solutions.