Question

graph the system on a separate sheet of paper and determine the number of solutions it has. if it has one solution, determine its coordinates.
$2x + 2y = 4$
$y = 2x - 1$
a) infinitely many solutions
b) 1 solution; (2,3)
c) no solution
d) 1 solution; (1, 1)

Explanation:

Step1: Substitute $y$ into first equation

Substitute $y=2x-1$ into $2x+2y=4$:
$2x + 2(2x-1) = 4$

Step2: Simplify and solve for $x$

Expand and combine like terms:
$2x + 4x - 2 = 4$
$6x - 2 = 4$
$6x = 6$
$x = 1$

Step3: Find $y$ using $x=1$

Substitute $x=1$ into $y=2x-1$:
$y = 2(1) - 1 = 1$

Step4: Verify the solution

Check $(1,1)$ in $2x+2y=4$:
$2(1) + 2(1) = 4$, which is true.

Answer:

D) 1 solution; (1, 1)