Solve the pair of equations $2x+3y=7$ and $x-y=1$ by the method of substitution.

Step-by-step solution

1. From the second equation, express $x$ as $x=y+1$ because substitution requires one variable in terms of the other.
2. Substitute $x=y+1$ into the first equation: $2(y+1)+3y=7$.
3. Simplify: $2y+2+3y=7\Rightarrow 5y+2=7$.
4. Subtract 2 from both sides: $5y=5$.
5. Divide by 5: $y=1$.
6. Substitute $y=1$ back into $x=y+1$ to get $x=2$.

Concept tested: Substitution method

Related questions

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