11x+10y=1100
101x-y=111
To solve the system of equations, we can use the method of substitution or elimination.
Method 1: Substitution
1) Solve one equation for one variable in terms of the other variable.
From the second equation, we have y = 101x - 111.
2) Substitute this expression for y into the other equation.
11x + 10(101x - 111) = 1100
11x + 1010x - 1110 = 1100
1021x - 1110 = 1100
1021x = 2210
x = 2210 / 1021
x ≈ 2.165
3) Substitute this value of x into either of the original equations and solve for y.
11 * 2.165 + 10y = 1100
23.815 + 10y = 1100
10y = 1100 - 23.815
10y = 1076.185
y = 1076.185 / 10
y ≈ 107.619
Therefore, the solution to the system of equations is approximately x ≈ 2.165 and y ≈ 107.619.
Method 2: Elimination
1) Multiply the second equation by 10 to eliminate the y term.
1010x - 10y = 1110
2) Add the equations together to eliminate the y term.
11x + 1010x - 10y = 1100 + 1110
1021x - 10y = 2210
3) Solve this equation for x.
1021x = 2210 + 10y
x = (2210 + 10y) / 1021
4) Substitute this expression for x into one of the original equations and solve for y.
11((2210 + 10y) / 1021) + 10y = 1100
(24310 + 110y) / 1021 + 10y = 1100
24310 + 110y + 10210y = 1100 * 1021
24310 + 11320y = 1122200
11320y = 1122200 - 24310
11320y = 1097890
y = 1097890 / 11320
y ≈ 97.074
5) Substitute this value of y into one of the original equations and solve for x.
11x + 10(97.074) = 1100
11x + 970.74 = 1100
11x = 1100 - 970.74
x = (1100 - 970.74) / 11
x ≈ 11.884
Therefore, the solution to the system of equations is approximately x ≈ 11.884 and y ≈ 97.074.
To solve this system of equations, we can use either substitution or elimination method. Let's use the elimination method:
Step 1: Multiply the second equation by 10 to make the coefficients of y in both equations the same:
10 * (101x - y) = 10 * 111
1010x - 10y = 1110
Step 2: Rewrite the system of equations:
11x + 10y = 1100
1010x - 10y = 1110
Step 3: Add the two equations together to eliminate the y variable:
(11x + 10y) + (1010x - 10y) = 1100 + 1110
11x + 1010x = 2210
1021x = 2210
Step 4: Solve for x by dividing both sides of the equation by 1021:
x = 2210 / 1021 ≈ 2.165
Step 5: Substitute the value of x into one of the original equations to solve for y. Let's use the first equation:
11(2.165) + 10y = 1100
23.815 + 10y = 1100
10y = 1100 - 23.815
10y = 1076.185
y = 1076.185 / 10 ≈ 107.619
So, the solution to the system of equations is x ≈ 2.165 and y ≈ 107.619.