Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this.
11x + 8y = 103
22x – 7y = 68
Solve the system for x and y. Show your work
x + y = 22
x - y = 6
11x+8y=103 (1)
22x-7y=68 (2)
Multiply (1) by -2 to cancel the x's
-22-16y=-206 (3)
22x-7y=68 (2)
Add them together.
-23y=-138
Divide by -23
y=6
Now substitute y=6 into either equation (1) or (2) to solve for x.
Post your work and answer if you'd like it checked.
Hi Jen,
Okay here is what I got to solve for x
11x *6 + 8y = 72
66 + 8y
8y = 9
x = 9
Okay did I do this right?
To solve the system of equations using the elimination method, we'll eliminate one variable by multiplying one or both equations by a constant, so the coefficients of one variable will be equal but with opposite signs. Let's follow the steps:
Step 1: Multiply one or both equations by a constant to make the coefficients of one variable equal but with opposite signs. In this case, we can multiply the first equation by 2 to obtain opposite coefficients for 'x'.
2(11x + 8y) = 2(103)
22x + 16y = 206
The system of equations becomes:
22x + 16y = 206
22x – 7y = 68
Step 2: Subtract the equations to eliminate one variable. We'll subtract the second equation from the first equation.
(22x + 16y) - (22x – 7y) = (206) - (68)
22x + 16y - 22x + 7y = 206 - 68
23y = 138
Step 3: Solve for the remaining variable. Divide both sides of the equation by 23.
23y/23 = 138/23
y = 6
Step 4: Substitute the value of 'y' back into one of the original equations and solve for 'x'. Let's use the first equation.
11x + 8(6) = 103
11x + 48 = 103
11x = 103 - 48
11x = 55
x = 5
Step 5: Check the solution by substituting the values of 'x' and 'y' back into the second equation, and see if it holds true.
22(5) - 7(6) = 68
110 - 42 = 68
68 = 68
The solution to the system of equations is x = 5 and y = 6.
Therefore, the answer is x = 5 and y = 6.