please giveme step by step instructions on how to solve linear equations.
-x+4y=9 and x-y=3 . I am trying to plot the coordinaces.
To solve the system of linear equations -x + 4y = 9 and x - y = 3 and plot the coordinates, follow these steps:
Step 1: Choose one of the equations and solve for one variable in terms of the other. Let's solve the second equation for x in terms of y:
x - y = 3
x = y + 3
Step 2: Substitute the expression for x in terms of y into the other equation. We will use the first equation for this:
-(-y + 3) + 4y = 9
y - 3 + 4y = 9
5y - 3 = 9
5y = 12
y = 2.4
Step 3: Substitute the value of y back into the equation we found in Step 2 to solve for x:
x = y + 3
x = 2.4 + 3
x = 5.4
The solution to the system of equations is x = 5.4 and y = 2.4.
Step 4: Plot the coordinates (5.4, 2.4) on a coordinate plane. The x-coordinate (5.4) represents horizontal distance, and the y-coordinate (2.4) represents vertical distance. Mark the point (5.4, 2.4) on the plane.
Step 5: To draw the line representing the equation -x + 4y = 9, rearrange the equation to the slope-intercept form (y = mx + b):
-(-x + 4y) = 9
x - 4y = 9
-4y = -x + 9
y = (1/4)x - 9/4
The equation is now in the form y = mx + b, where the coefficient of x (m) represents the slope and the constant term (b) represents the y-intercept.
Step 6: Starting from the point (5.4, 2.4) on the coordinate plane, use the slope of 1/4 to find another point on the line. For example, by moving one unit to the right (horizontal) and four units up (vertical), we can find a second point (6.4, 6.4) on the line.
Step 7: Connect the two points (5.4, 2.4) and (6.4, 6.4) with a straight line. This line represents the equation -x + 4y = 9.
Now you have solved the system of equations and plotted the coordinates.