One solution:
4x+22=8x+10
5x+5=5x+4
1.Consider the two equations that you underlined, which form a system with one solution.
2.Solve the equations.
3.What do you notice about these equations?
5.What does it mean to have one solution?
6.Plug a few points into the original equations and check to show that the system of equations has one solution.
Explain your work.
2. To solve the system of equations, we can start by subtracting 4x from both sides of the first equation:
22 = 4x + 10
12 = 4x
x = 3
Now we can plug this value of x back into one of the original equations to solve for y. Let's use the second equation:
5(3) + 5 = 5y + 4
15 + 5 = 5y + 4
20 = 5y + 4
16 = 5y
y = 3.2
So the solution to the system of equations is x = 3 and y = 3.2.
3. These equations intersect at a single point, which means they have one solution.
5. Having one solution means that the two lines represented by the equations intersect at a single point on the coordinate plane.
6. To verify that the system has one solution, we can plug the values of x = 3 and y = 3.2 back into the original equations:
First equation:
4(3) + 22 = 8(3) + 10
12 + 22 = 24 + 10
34 = 34
Second equation:
5(3) + 5 = 5(3) + 4
15 + 5 = 16
20 = 20
Both equations hold true when we substitute the values of x = 3 and y = 3.2, confirming that the system of equations has a unique solution.