Fill in the blank/s: When solving x = 3y + 2 and 5x - 15y = 10 by the substitution method, we obtain 10 = 10, so the solution set is ___________ The equations in this system are called ___________ . If you attempt to solve such a system by graphing, you will obtain two lines that ___________

Fill in the blank/s: When solving x = 3y + 2 and 5x - 15y = 10 by the substitution method, we obtain 10 = 10, so the solution set is ___________ The equations in this system are called ___________ . If you attempt to solve such a system by graphing, you will obtain two lines that ___________

Question
Equations and inequalities
asked 2020-12-28
Fill in the blank/s: When solving x = 3y + 2 and 5x - 15y = 10 by the substitution method, we obtain 10 = 10, so the solution set is ___________ The equations in this system are called ___________ . If you attempt to solve such a system by graphing, you will obtain two lines that ___________

Answers (1)

2020-12-29
Given equations are
\(\displaystyle{X}={3}{Y}+{2}\)
\(\displaystyle{X}-{3}{Y}={2}---{\left({1}\right)}\)
\(\displaystyle{5}{X}-{15}{Y}={10}---{\left({2}\right)}\)
\(\displaystyle{\frac{{{a}_{{1}}}}{{{a}_{{2}}}}}={\frac{{{1}}}{{{5}}}},{\frac{{{b}_{{1}}}}{{{b}_{{2}}}}}={\frac{{-{3}}}{{-{15}}}}={\frac{{{1}}}{{{5}}}}{\quad\text{and}\quad}{\frac{{{c}_{{1}}}}{{{c}_{{2}}}}}={\frac{{{2}}}{{{10}}}}={\frac{{{1}}}{{{5}}}}\)
\(\displaystyle{w}{e}{k}{n}{o}{w}{t}\hat{{w}}{h}{e}{n}{\frac{{{a}_{{1}}}}{{{a}_{{2}}}}}={\frac{{{b}_{{1}}}}{{{b}_{{2}}}}}={\frac{{{c}_{{1}}}}{{{c}_{{2}}}}}\)
then given lines have infinite number of solutions
And given line will be coincident lines.
Hence, solution set will be infinite.The equation are in this system are called coincident . And we will draw graph then line will coincide with each other
0

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Fill in the bla
so the resulting statement is true.
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Fill in the bla
so the resulting statement is true
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