# Using substitution method solve 3x+4y=7 2x-3y=-1

Question
Linear equations and graphs
Using substitution method solve
$$\displaystyle{3}{x}+{4}{y}={7}$$
$$\displaystyle{2}{x}-{3}{y}=-{1}$$

2021-02-12
From the second equation, $$\displaystyle{2}{x}={3}{y}-{1}$$, so $$\displaystyle{x}=\frac{{{3}{y}-{1}}}{{2}}.$$
Substitute for x in the first equation:
$$\displaystyle{3}\frac{{{3}{y}-{1}}}{{2}}+{4}{y}={7}$$, multiply each side by 2:
$$\displaystyle{3}{\left({3}{y}-{1}\right)}+{8}{y}={14},{9}{y}-{3}+{8}{y}={14},{17}{y}={17},{y}={1},$$ therefore $$\displaystyle{x}=\frac{{{3}-{1}}}{{2}}=\frac{{2}}{{2}}={1}$$.
Solution: x=1, y=1.

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