Answer:
Explanation:
To solve the system of linear equations using the addition/elimination method, you can manipulate the equations to eliminate one of the variables. Here's how you can do it:
Start with the original equations:
9x - 5y = -30 ...(1)
x + 3y = 18 ...(2)
To eliminate one of the variables, let's eliminate "x." Multiply equation (2) by 9 so that the coefficients of "x" in both equations become equal:
9(x + 3y) = 9(18)
This simplifies to:
9x + 27y = 162 ...(3)
Now, you have the modified equation (3) and the original equation (1). You can subtract equation (1) from equation (3) to eliminate "x":
(9x + 27y) - (9x - 5y) = 162 - (-30)
9x + 27y - 9x + 5y = 162 + 30
Combine like terms:
32y = 192
Divide by 32 to solve for "y":
y = 192 / 32
y = 6
Now that you have the value of "y," you can substitute it into equation (2) to solve for "x":
x + 3y = 18
x + 3(6) = 18
x + 18 = 18
Subtract 18 from both sides:
x = 0
So, the solution to the system of equations is:
x = 0
y = 6
Now, you can graphically represent this solution by plotting the point (0, 6) on a coordinate plane. This is the point where the two lines representing the equations intersect.
Here's how the equations look when graphed:
Equation (1): 9x - 5y = -30
Equation (2): x + 3y = 18
The point of intersection is (0, 6).