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Identify which equations have one solution, infinitely many solutions, or no solution.3u+40+2+ = 60-30-u2.2z+3z = 4.5–3.2 $$+$+fr = 12.3y+3.2–y=2.1+1.3y+1.1 5+3+s=ſr 20+49 = 32–2rNo SolutionOne SolutionInfinitely Many Solutions

Identify which equations have one solution, infinitely many solutions, or no solution-example-1

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Answer:

No Solution: Top- left, Top, Right

One Solution: Top - middle, Bottom -Middle, Bottom - right.

Infinitely Many solutions: Bottom- left,

Explanation:

If an equation has one solution, then the left-hand side of the equation does not equal the right-hand side.

If an equation has no solution then the slopes are the same for right and left equations; however, the intercepts are not the same. For example 3x -3 = 3x -5 has no solutions.

If an equation has infinitely many solutions, then the equation on the right is equal to the equation on the left. For example, 4x +5 = 2x + 2x + 5 which implies to 4x + 5 = 4x + 5 and therefore, it has infinitely many solutions.

With this knowledge in mind, we simplify each of the equations given.

For example, for the equation on the Top- left


3u+40+2u=6u-3-u

Simplifying both sides (adding like terms ) gives


5u+40=5u-3

The expressions on both sides of the equality sign have the same slopes but different y-intercepts; therefore, this equation has no solutions - when graphed lines 5u + 40 and 5u - 3 will never intersect.

The same goes for other equations, and in simplifying them we get the answers:

No Solution: Top- left, Top, Right

One Solution: Top - middle, Bottom -Middle, Bottom - Right.

Infinitely Many solutions: Bottom- left,

User RHertel
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