Solve: x-3y=-9
4x+3y=-6
x - 3y = -9
-3y = -9 - x Multiply with -1
3y = 9 + x
4x + 3y= -6
4x + 9 + x = -6
5x + 9 = -6
5x = -6 - 9
5x = -15 Divide with 5
x= -15/5
x= -3
3y=9 + x
3y = 9 +(-3)
3y = 9 - 3
3y = 6 Divide with 3
y = 6/3
y= 2
Solution:
x = -3
y = 2
If we note that there is a +3y and a -3y in each of the equations, we simply add the two equations to get:
5x=-15, or x=-3
Substitute x=-3 in either one of the equations to get
-3-3y=-9
-3y=-6
y=2
To solve the given system of equations:
1. Let's start by using the elimination method. Multiply the first equation by 4, and multiply the second equation by -1 to cancel out the y terms:
4(x - 3y) = 4(-9) [multiply the first equation by 4]
-1(4x + 3y) = -1(-6) [multiply the second equation by -1]
Simplifying these equations gives us:
4x - 12y = -36
-4x - 3y = 6
2. Add the two equations together to eliminate the x terms:
(4x - 12y) + (-4x - 3y) = -36 + 6
4x - 12y - 4x - 3y = -30
Simplifying this equation gives us:
-15y = -30
3. Divide both sides of the equation by -15 to solve for y:
-15y / -15 = -30 / -15
y = 2
4. Substitute the value of y (which we found in step 3) in either of the original equations to solve for x. Let's use the first equation:
x - 3(2) = -9
x - 6 = -9
x = -9 + 6
x = -3
Therefore, the solution to the system of equations is x = -3 and y = 2.