{−5x+y=−2−3x+6y=−12
{−5x+y=−33x−8y=24
{x+y=2−x+2y=16
{−4x+y=6−5x−y=21
There are different methods to solve systems of linear equations, but one common way is to use elimination to isolate one variable and then substitute it into the other equation. Here are the solutions for each system:
{−5x+y=−2
−3x+6y=−12
From the first equation, we can solve for y:
y = 5x - 2
Then substitute this into the second equation:
-3x + 6(5x - 2) = -12
27x = 18
x = 2/3
Finally, use the first equation to find y:
-5(2/3) + y = -2
y = 8/3
The solution is (2/3, 8/3).
{−5x+y=−33x−8y=24
To use elimination, we want to eliminate one variable by multiplying one or both equations by a constant. Let's eliminate y by multiplying the first equation by 8 and the second equation by 1:
-40x + 8y = -24
3x - 8y = 24
Adding these two equations eliminates y:
-37x = 0
x = 0
Then use either equation to solve for y:
-5(0) + y = -3
y = -3
The solution is (0, -3).
{x+y=2
−x+2y=16
From the first equation, we can solve for x:
x = 2 - y
Then substitute this into the second equation:
-(2 - y) + 2y = 16
y = 14
Finally, use the first equation to find x:
x + 14 = 2
x = -12
The solution is (-12, 14).
{−4x+y=6
−5x−y=21
To eliminate y, we can add the two equations:
-9x = 27
x = -3
Then use either equation to solve for y:
-4(-3) + y = 6
y = 18
The solution is (-3, 18).