how do you solve the system x-y=11 and y=-2x+19
To solve the system:
x - y = 11
y = -2x + 19
You can substitute the second equation into the first by replacing y with -2x + 19:
x - (-2x + 19) = 11
Simplifying:
x + 2x - 19 = 11
Combining like terms:
3x - 19 = 11
Add 19 to both sides:
3x = 30
Divide both sides by 3:
x = 10
Now that you have the value of x, you can substitute it back into one of the original equations to find y. Using the second equation:
y = -2(10) + 19
Simplifying:
y = -1
Therefore, the solution to the system is x = 10 and y = -1.