Answer: To find the values of x and y that satisfy the system of equations:
2x - y = 10 (Equation 1)
x + y = 11 (Equation 2)
One way to solve this system is by using the method of substitution.
From Equation 2, we can isolate x by subtracting y from both sides:
x = 11 - y
Now, substitute this value of x into Equation 1:
2(11 - y) - y = 10
Simplify the equation:
22 - 2y - y = 10
22 - 3y = 10
Next, isolate y by subtracting 22 from both sides:
-3y = 10 - 22
-3y = -12
Divide both sides by -3 to solve for y:
y = -12 / -3
y = 4
Now that we have the value of y, substitute it back into Equation 2 to find the value of x:
x + 4 = 11
Subtract 4 from both sides:
x = 11 - 4
x = 7
Therefore, the solution to the system of equations is x = 7 and y = 4.
You can check this solution by substituting the values of x and y back into the original equations. If the left side of each equation equals the right side, then the solution is correct.