Understanding Linear Equations: Breaking Down the Equation Ax + By = C

Ax+By=C

The equation Ax + By = C represents a linear equation in two variables, x and y

The equation Ax + By = C represents a linear equation in two variables, x and y. In this equation, A, B, and C are constants.

To further understand this equation, let’s break it down:

– A is the coefficient of the x-variable, indicating the amount by which x is being multiplied.
– B is the coefficient of the y-variable, indicating the amount by which y is being multiplied.
– C is a constant term, representing the total value on the other side of the equation.

This equation can be thought of as the equation of a line in a two-dimensional coordinate system. Here, x and y are the variables, and A, B, and C determine the slope and intercept of the line.

To graph this equation, we can use the slope-intercept form (y = mx + b) by rearranging the given equation:

Ax + By = C

By = -Ax + C

y = (-A/B)x + (C/B)

So, the slope of the line would be -A/B, and the y-intercept would be C/B.

To solve the equation for specific values of x and y, we need additional information. If more equations with the same variables are given, it may be possible to solve for the simultaneous values that satisfy all the equations.

Alternatively, if the equation is given with specific values for A, B, and C, you could substitute those values and solve for x and y.

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