Question

2x+=2x+7 3x+18=5x+8

Plug a few points into the original equations and check to show that the system of equations has one solution. Explain your work.

Answer 1

First, let's solve the system of equations:

Equation 1: 2x+ = 2x+7
Equation 2: 3x+18 = 5x+8

To solve this system, let's work on eliminating one variable from one of the equations. To do this, we can subtract equation 1 from equation 2:

(3x+18)-(2x+7) = (5x+8)-(2x+7)

Simplify the equation:

x+11 = 3x+1

Now, subtract x from both sides and subtract 1 from both sides:

11-1 = 3x-x

10 = 2x

Now, divide both sides by 2:

x = 5

Now that we have x, we can find y by plugging x into one of the original equations. Let's use equation 1:

2(5)+y = 2(5)+7

10+y = 10+7

y = 7

Therefore, the solution to this system of equations is x = 5 and y = 7. Let's now check these values in the original equations:

Equation 1: 2x+y = 2x+7
2(5)+7 = 2(5)+7
17 = 17 (True)

Equation 2: 3x+18 = 5x+8
3(5)+18 = 5(5)+8
33 = 33 (True)

Since these points satisfy both equations, we can conclude that the system has one solution, which is (x, y) = (5, 7).