Does the system of equations have no solution, one solution, or infinitely many solutions?
y = x + 4
y – 4 = x
if you rearrange terms, you have
y = x+4
y = x+4
they are the same equation, so there are infinitely many solutions. Whatever point is on one graph is also on the other.
To determine whether the system of equations has no solution, one solution, or infinitely many solutions, we need to compare the coefficients of the variables.
Let's write the system of equations in standard form:
Equation 1: y = x + 4
Equation 2: y - 4 = x
In standard form, we rewrite the equations so that the variables (x and y) are on the left side and the constants are on the right side.
To compare the coefficients, we need to look at the slopes of the equations. The slope of a linear equation is the coefficient of x (since x is the variable that determines the change in y).
Equation 1: y = x + 4
The coefficient of x is 1, so the slope is 1.
Equation 2: y - 4 = x
We rewrite this equation in slope-intercept form by adding 4 to both sides:
y = x + 4
The coefficient of x is also 1, so the slope is 1.
Since the slopes of both equations are the same (1), the lines are parallel. When two lines are parallel, they will never intersect, and therefore, there is no solution.