I need help with these problem someone told me that you was not helping them.
Please help me!!
5/4x +1/8x=11/8 +x
The solution is x=
Solve by the elimination method.
4x +5y=5
8x +10y=10
What is the solution of the system.
for the first, multiply each term by 8,
easy after that.
for the second, there is an infinite number of solutions.
Notice if you double the first equation, you get exactly the second equation.
So really you are just given the same equation twice.
So, any x and y which satisfies the equation is a solution,
e.g.
x = 0, y = 1
x
Sure, I'd be happy to help you with these problems!
Let's start with the first problem:
5/4x + 1/8x = 11/8 + x
To solve this equation using the elimination method, we need to get rid of the fractions. One way to do this is by multiplying the entire equation by the least common denominator (LCD) of the fractions involved, which in this case is 8.
Multiply both sides of the equation by 8:
8 * (5/4x + 1/8x) = 8 * (11/8 + x)
Simplifying the equation, we have:
10x + x = 11 + 8x
Combining like terms, we get:
11x = 11 + 8x
Next, we want to isolate the variable on one side of the equation. We can do this by subtracting 8x from both sides:
11x - 8x = 11 + 8x - 8x
Simplifying further, we have:
3x = 11
Now, to solve for x, we need to divide both sides of the equation by the coefficient of x, which is 3:
3x/3 = 11/3
This simplifies to:
x = 11/3
Therefore, the solution to the equation is x = 11/3.
Now let's move on to the second problem:
4x + 5y = 5
8x + 10y = 10
To solve this system of equations using the elimination method, we need to eliminate one variable by adding or subtracting the equations. In this case, we can manipulate the first equation to simplify it and use it for elimination.
Multiply the first equation by 2 to make the coefficients of x in both equations match:
2 * (4x + 5y) = 2 * 5
This simplifies to:
8x + 10y = 10
Now we have a system of equations with the same coefficient for x. We can subtract the second equation from the modified version of the first equation:
(8x + 10y) - (8x + 10y) = 10 - 10
This simplifies to:
0 = 0
Since both equations result in a true statement (0 = 0), we have dependent equations. This means that the two equations represent the same line and have an infinite number of solutions. In other words, any values of x and y that satisfy one equation will also satisfy the other equation.
Therefore, the solution to the system of equations is an infinite number of ordered pairs (x, y) that satisfy the equations.