Match the description of the one variable equation with the number of solutions it will have.
ax+c1=bx+c2
a
x
+
c
1
=
b
x
+
c
2
(3 points)
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The number of x's on both sides of the equation is different a≠b
The number of x's is the same on both sides of the equation, and the constant is different a=b, c1≠c2
The number of x's is the same on both sides of the equation and the constant is also the same a=b, c1=c2
No SolutionOne SolutionTwo SolutionsThree SolutionsInfinite Solutions
The number of x's on both sides of the equation is different a≠b - One Solution
what about the other ones
The number of x's is the same on both sides of the equation, and the constant is different a=b, c1≠c2 - No Solution
The number of x's is the same on both sides of the equation and the constant is also the same a=b, c1=c2 - Infinite Solutions
The number of x's is the same on both sides of the equation and the constant is also the same (a=b, c1=c2)
To determine the number of solutions for the one-variable equation ax + c1 = bx + c2, we need to compare the coefficients and constants on both sides of the equation.
If the number of x's is different on both sides of the equation (a ≠ b), then there will be one solution. This means that the equation represents a single point of intersection between the two lines represented by the equation.
If the number of x's is the same on both sides of the equation (a = b) and the constants are different (c1 ≠ c2), then there will be no solution. This means that the lines represented by the equation are parallel and will never intersect.
If the number of x's is the same on both sides of the equation (a = b) and the constants are also the same (c1 = c2), then there will be infinite solutions. This means that the lines represented by the equation are coincident and will have an infinite number of points of intersection.
So, let's match the description of the equation ax + c1 = bx + c2 with the corresponding number of solutions:
- The number of x's on both sides of the equation is different (a ≠ b): One Solution.
- The number of x's is the same on both sides of the equation and the constant is different (a = b, c1 ≠ c2): No Solution.
- The number of x's is the same on both sides of the equation and the constant is also the same (a = b, c1 = c2): Infinite Solutions.
Therefore, the matching descriptions are as follows:
ax + c1 = bx + c2 --> One Solution