Solve each system using substitution. tell whether the system has one solution, infinitely many solutions, or no Solution.
1.) y=2x -1
2x +2y= 22
since y=2x-1,
2x + 2(2x-1) = 22
6x = 24
x = 4
so, y = 2x-1 = 7
one solution.
To solve the system of equations using substitution, we need to substitute the value of y from the first equation into the second equation.
Step 1: Solve the first equation for y
y = 2x - 1
Step 2: Substitute the value of y into the second equation
2x + 2(2x - 1) = 22
Step 3: Simplify and solve for x
2x + 4x - 2 = 22
6x - 2 = 22
6x = 24
x = 4
Step 4: Substitute the value of x back into the first equation to find y
y = 2(4) - 1
y = 8 - 1
y = 7
Therefore, the solution to the system of equations is x = 4 and y = 7. The system has one solution.
To solve this system using substitution, we can start by rearranging the first equation to solve for "y":
y = 2x - 1
We can substitute this expression for "y" in the second equation:
2x + 2(2x - 1) = 22
Now, simplify and solve for "x":
2x + 4x - 2 = 22
6x - 2 = 22
6x = 24
x = 4
Next, substitute the value of "x" into the first equation to solve for "y":
y = 2(4) - 1
y = 8 - 1
y = 7
Now we have found values for both "x" and "y", so this system has one unique solution.
The solution to this system is x = 4 and y = 7.