Solve the linear equation. Solve for x and y
y=-3/4x + 1/4
y=3/4x - 3/4
add the two equations to get y alone:
y = -3/4x + 1/4
y = 3/4x - 3/4
--------------------------
2y = -2/4
y = -1/4
then substitute this value of y to either of the equations and solve for x. in this case let's substitute this to the first give equation:
y = -3/4x + 1/4
-1/4 = -3/4x + 1/4
-1/4 - 1/4 = -3/4x
(-2/4 = -3/4x)*4
-2 = -3x
x = 2/3
hope this helps~ :)
To solve the given system of linear equations, we'll use the method of substitution. The goal is to isolate one variable in terms of the other and then substitute the expression into the other equation.
Let's start by isolating the variable "y" in terms of "x" in the first equation:
y = -3/4x + 1/4
Next, we'll substitute this expression for "y" in the second equation:
(Replacing "y" with the expression we found)
3/4x - 3/4 = 3/4x - 3/4
Now we have an equation with only one variable, "x". Let's solve for "x":
3/4x - 3/4 = 3/4x - 3/4
To eliminate the fractions, we can multiply everything by the least common denominator, which is 4.
4 * (3/4x - 3/4) = 4 * (3/4x - 3/4)
Simplifying the equation gives:
3x - 3 = 3x - 3
Now, the "x" terms on both sides of the equation cancel out, leaving us with:
-3 = -3
This equation is true, which means that there are infinitely many solutions to the system of equations.
So, we can assign any value to "x" and find the corresponding value of "y" using either of the original equations. For example, let's assign "x" a value of 0:
Using the first equation:
y = -3/4(0) + 1/4
y = 0 + 1/4
y = 1/4
Therefore, when x = 0, y = 1/4.