How many solutions does the system of equations below have? {:[-10 y-2=-5x],[14 y+6=2x]:} (A) no solution (B) one solution (C) infinitely many solutions

Question

Bytelearn · Accepted Answer

Write Equations: Write down the system of equations. We have the following system of equations: -10y - 2 = -5x 14y + 6 = 2xRearrange for x: Rearrange each equation to express x in terms of y. For the first equation, we can divide both sides by -5 to isolate x: -10y - 2 = -5x x = (10y + 2) / 5 For the second equation, we can divide both sides by 2 to isolate x: 14y + 6 = 2x x = (14y + 6) / 2Compare x Expressions: Compare the expressions for x obtained from both equations. From the first equation, we have: x = 2y + 0.4 From the second equation, we have: x = 7y + 3Check Equivalency: Determine if the two expressions for x are equivalent. Since 2y + 0.4 is not the same as 7y + 3, the expressions for x are not equivalent. This means that the lines represented by the two equations are not the same line.Check Parallel Lines: Check if the two lines are parallel. To check if the lines are parallel, we compare their slopes. The slope of the first line is 2, and the slope of the second line is 7. Since the slopes are not equal, the lines are not parallel.Conclude Number of Solutions: Conclude the number of solutions based on the comparison. Since the lines are not the same and they are not parallel, they must intersect at exactly one point. Therefore, the system of equations has one solution.

How many solutions does the system of equations below have? $\newline$ $\begin{array}{l} -10 y-2=-5 x \\ 14 y+6=2 x \end{array}$ $\newline$ (A) no solution $\newline$ (B) one solution $\newline$ (C) infinitely many solutions

Full solution

More problems from Checkpoint: Rational and irrational numbers

Related topics

How many solutions does the system of equations below have?\newline−10y−2=−5x14y+6=2x \begin{array}{l} -10 y-2=-5 x \\ 14 y+6=2 x \end{array} −10y−2=−5x14y+6=2x​\newline(A) no solution\newline(B) one solution\newline(C) infinitely many solutions

How many solutions does the system of equations below have? $\newline$ $\begin{array}{l} -10 y-2=-5 x \\ 14 y+6=2 x \end{array}$ $\newline$ (A) no solution $\newline$ (B) one solution $\newline$ (C) infinitely many solutions