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Answer :
To solve the given system of equations using the method of elimination, let's first take a closer look at the equations:
1. [tex]\(5a + 5b = 25\)[/tex]
2. [tex]\(5a + 5b = 35\)[/tex]
To use the elimination method, we can subtract the first equation from the second equation to eliminate both [tex]\(a\)[/tex] and [tex]\(b\)[/tex]:
[tex]\[
(5a + 5b) - (5a + 5b) = 35 - 25
\][/tex]
Simplifying both sides, we get:
[tex]\[
0 = 10
\][/tex]
This equation [tex]\(0 = 10\)[/tex] is a contradiction, which means there is no possible value of [tex]\(a\)[/tex] and [tex]\(b\)[/tex] that will satisfy both original equations simultaneously. Therefore, the system of equations is inconsistent and has no solution.
In summary, when using the elimination method, we found that the resulting equation is contradictory, indicating that there is no solution to the system of equations.
1. [tex]\(5a + 5b = 25\)[/tex]
2. [tex]\(5a + 5b = 35\)[/tex]
To use the elimination method, we can subtract the first equation from the second equation to eliminate both [tex]\(a\)[/tex] and [tex]\(b\)[/tex]:
[tex]\[
(5a + 5b) - (5a + 5b) = 35 - 25
\][/tex]
Simplifying both sides, we get:
[tex]\[
0 = 10
\][/tex]
This equation [tex]\(0 = 10\)[/tex] is a contradiction, which means there is no possible value of [tex]\(a\)[/tex] and [tex]\(b\)[/tex] that will satisfy both original equations simultaneously. Therefore, the system of equations is inconsistent and has no solution.
In summary, when using the elimination method, we found that the resulting equation is contradictory, indicating that there is no solution to the system of equations.
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