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.
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.
1 answer
1 answer