Question

Solve the following pair of linear equations by the elimination method and the substitution method:x + y = 5, 2x - 3y = 4

Matrix transformations
ANSWERED
asked 2021-01-19

Solve the following pair of linear equations by the elimination method and the substitution method:
\(x + y = 5, 2x - 3y = 4\)

Expert Answers (1)

2021-01-20

Given:
\(x+y=5 \rightarrow\)(1)
\(2x-3y=4 \rightarrow\)(2)
solution by elimination method:
\([2 \cdot equation(1)]-[equation(2)]\)
\(\Rightarrow 2(x+y)-(2x-3y)=2(5)-4\)
\(\Rightarrow 5y=6\)
\(\Rightarrow y=6/5\)
\(\Rightarrow y=1.2\)
now substituting \(y=1.2\) in equation(1),we ge
\(x+1.2=5 \Rightarrow x=3.8\)
\(x=3.8\) and \(y=1.2\)
solution by substitution method
From equation \(\rightarrow\)(1), we have
\(x+y=5 \Rightarrow y=5-x\)
now substituting \(y=5-x\) in equation(2), we get
\(2x-3(5-x)=4 \Rightarrow 2x-15+3x=4 \Rightarrow 5x=19 \Rightarrow x=3.8\)
now substituting \(x=3.8+\) in equation (1),we get
\(3.8+y=5 \Rightarrow y=1.2\)
\(x=3.8\) and \(y=1.2\)

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