Question

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

Matrix transformations

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

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 $$y=1.2$$