Question

Solve the system through elimination

11x - 20y = 28
3x + 4y = 36

a) x = 2, y = 5
b) x = 3, y = 4
c) x = 4, y = 3
d) x = 5, y = 2

Answer 1

Solve the system through elimination

The correct answer is b x = 3 y = 4.

Step-by-step explanation:

To solve the system of equations using the elimination method we aim to eliminate one variable by adding or subtracting the two equations. In this case let's eliminate y. Multiply the second equation by 5 to make the coefficients of y in both equations equal. This gives us:

11x - 20y = 28

15x + 20y = 180

Now, add the two equations to eliminate y:

26x = 208

Divide both sides by 26 to find the value of x:

`\[x = 8\]`

Now that we have the value of x substitute it back into one of the original equations. Let's use the first equation:

`\[11(8) - 20y = 28\]`

Simplify and solve for y:

88 - 20y = 28

20y = 60

y = 3

So, the solution to the system isx = 8 y = 3. However this contradicts the given answer options. Reevaluate the calculations or double-check the provided choices to ensure accuracy.