Question

Without​ graphing, decide whether the system of equations has one​ solution, no​ solution, or infinitely many solutions.
y equals 2 x plus 10
y equals negative 2 x plus 10
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Part 1
How many solutions does the system of equations​ have?
One solution
Infinitely many solutions
No solution

Answer 1

One solution.

The slopes are different (2 and -2), so the lines intersect exactly once. Solving 2x + 10 = -2x + 10 gives 4x = 0, x = 0, and y = 10, so the intersection is (0, 10).