Question

4x+22=8x+10 5x+5=5x+4

Plug a few points into the original equations and check to show that they can have no
solution. Explain your work.

Answer 1

Let's first solve both equations:

Equation 1:
4x + 22 = 8x + 10

Subtract 4x from both sides:
22 = 4x + 10

Subtract 10 from both sides:
12 = 4x

Divide by 4:
x = 3

Equation 2:
5x + 5 = 5x + 4

Subtract 5x from both sides:
5 = 4

As we can see, equation 2 gives us a false statement (5 does not equal 4), which means there is no consistent solution for x that satisfies both equations. In other words, these two equations are inconsistent, and there is no solution.

We can verify this by plugging in x = 3 into both equations and checking if they are true:

Equation 1: 4(3) + 22 = 12 + 22 = 34, and 8(3) + 10 = 24 + 10 = 34, so the left-hand and right-hand sides of the equation are equal.

Equation 2: 5(3) + 5 = 15 + 5 = 20, and 5(3) + 4 = 15 + 4 = 19, so the left-hand and right-hand sides of the equation are not equal.

Since the values do not satisfy both equations, there is no solution to this system of linear equations.