10x+15y=20
-9x-15y=-21
You can solve this system of equations in many ways.
This easiest way, in my opinion, is by addition.
10x+15y=20
+
-9x-15y=-21
---------------------
x=-1
Now you have x = -1
plug that into any of the equations to get y
You can also solve this with substitution as well.
To solve this system of equations, we can use the method of elimination or substitution.
Let's use the method of elimination to eliminate the "y" term.
Step 1: Multiply both sides of the second equation by 5 to make the coefficient of "y" in both equations the same. This will allow us to cancel out the "y" term when we add the equations together.
So, the second equation becomes: -45x - 75y = -105.
Now, we have the following system of equations:
10x + 15y = 20
-45x - 75y = -105
Step 2: Add the two equations together.
(10x + 15y) + (-45x - 75y) = 20 + (-105)
This simplifies to:
10x - 45x + 15y - 75y = -85
Combining like terms:
-35x - 60y = -85
Step 3: Divide every term by -5 to get the x-coefficient to be positive.
(-35x)/-5 - (60y)/-5 = (-85)/-5
This simplifies to:
7x + 12y = 17
So, the simplified system of equations is:
10x + 15y = 20
7x + 12y = 17
Now we can solve this system of equations using the method of substitution or elimination.
To find the solution to the system of equations:
10x + 15y = 20
-9x - 15y = -21
We will use the method of elimination:
Step 1: Multiply the second equation by 10, so that the coefficients of x in both equations have opposite signs:
-90x - 150y = -210
Step 2: Add the two equations together:
(10x + 15y) + (-90x - 150y) = 20 + (-210)
This simplifies to:
-80x = -190
Step 3: Divide both sides of the equation by -80:
x = -190 / -80
x = 19 / 8.75
Step 4: Substitute the value of x back into one of the original equations to solve for y. Let's use the first equation:
10(19 / 8.75) + 15y = 20
Simplify this equation:
19 / 0.875 + 15y = 20
Step 5: Solve for y:
19 / 0.875 = 20 - 15y
Multiply both sides of the equation by 0.875 to get rid of the fraction:
19 = (20 - 15y) * 0.875
Now, subtract 20 from both sides:
-1 = -15y * 0.875
Divide both sides by -15 * 0.875:
y = -1 / (-15 * 0.875)
y = 1 / 13.125
So, the solution to the system of equations is:
x = 19 / 8.75
y = 1 / 13.125