Respuesta :
Step-by-step explanation:
To determine the number of solutions for the equation -15x + 5y = 10, we need to analyze its characteristics.
This is a linear equation in two variables, x and y. The equation represents a straight line on a graph in the Cartesian coordinate system. The number of solutions depends on the relationship between the coefficients of x and y.
To find the number of solutions, we can first simplify the equation by dividing all terms by 5:
-15x/5 + 5y/5 = 10/5
This simplifies to:
-3x + y = 2
Now, we can rewrite this equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept:
y = 3x + 2
Since this equation is in slope-intercept form, we know it represents a straight line. The slope is 3, which means the line is upward-sloping, and the y-intercept is 2.
A linear equation with a non-zero slope and a y-intercept has an infinite number of solutions because every point on the line satisfies the equation.
Therefore, the equation -15x + 5y = 10 has infinitely many solutions.
