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Sagot :
The Slope-Intercept form of an equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope of the line and "b" is the y-intercept.
- The first equation given in the exercise is:
[tex]4x+3y=5[/tex]Solve for "y" in order to write it in Slope-Intercept form:
[tex]\begin{gathered} 3y=-4x+5 \\ y=-\frac{4}{3}x+\frac{5}{3} \end{gathered}[/tex]You can identify that:
[tex]\begin{gathered} m_1=-\frac{4}{3} \\ \\ b_1=\frac{5}{3} \end{gathered}[/tex]- The second equation is:
[tex]24x+3y=7[/tex]Solve for "y":
[tex]\begin{gathered} 3y=-24x+7 \\ \\ y=\frac{-24}{3}x+\frac{7}{3} \\ \\ y=-8x+\frac{7}{3} \end{gathered}[/tex]You can identify that:
[tex]\begin{gathered} m_2=-8 \\ \\ b_2=\frac{7}{3} \end{gathered}[/tex]- As you can notice, the lines are not parallel, because:
[tex]m_1\ne m_2[/tex]- The lines are not the the same line, because:
[tex]\begin{gathered} m_1\ne m_2 \\ b_1\ne b_2 \end{gathered}[/tex]- Therefore, since they are different ant they're not parallel, they will intersect each other at some point. This means that the System of equations has one solution.
The answer is: Option b.
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