Question

Solve a) with Substitution and b) with Elimination (check attached picture)

Answer 1

a) Solve the first equation for
`x`.

`x + 3y = 7 \impiles x = 7 - 3y`

Substitute this into the second equation and solve for
`y`.

`2x + 4y = 12 \implies 2(7 - 3y) + 4y = 12 \\\\ \implies 14 - 6y + 4y = 12 \\\\ \implies -2y = -2 \\\\ \implies \boxed{y=1}`

Solve for
`x`.

`x = 7 - 3y \implies x = 7-3*1 \\\\ \implies \boxed{x = 4}`

b) Eliminate
`y` by combining the two equations in appropriate parts, namely

`2 (2x - y) + (3x + 2y) = 2*3 + (-3)`

and solve for
`x`.

`2 (2x - y) + (3x + 2y) = 2*3 + (-3) \implies 4x - 2y + 3x + 2y = 6 - 3 \\\\ \implies 7x = 3 \\\\ \implies \boxed{x = \frac37}`

Solve for
`y`.

`2x - y = 3 \implies 2*\frac37 - y = 3 \\\\ \implies \frac67 - y = 3 \\\\ \implies -y = \frac{15}7 \\\\ \implies \boxed{y = -\frac{15}7}`