infinitely many solutions
Step-by-step explanation:
The given equations:
4x + 2y = 6 ...(1)
y = -2x + 3 ...(2)
To graph both equations, we can assing values to x in order to get the corresponding values of y
let x = -2, 0, 2
for 4x + 2y = 6
when x = -2
4(-2) + 2y = 6
2y = 6 + 8
y = 7
when x = 0
4(0) + 2y = 6
2y = 6
y = 3
when x = 2
4(2) + 2y = 6
2y = 6 - 8
y = -1
for y = -2x + 3
when x = -2
y = -2(-2) + 3
y = 4 + 3 = 7
when x = 0
y = -2(0) + 3
y = 0 + 3 = 3
when x = -2
y = -2(2) + 3
y = -4 + 3 = -1
plotting the graphs:
From the graph, we see the two equations overlap each other. This means the two equations are the same just that they were written differently.
From the values we got in each equation, we also see the y values are the same
Since both equations give same line, we will have infinitely many solutions