Question

Solve y=3x-7 and 4x+3y=18 by substitution

Answer 1

`\huge\boxed{x=3,\ y=2\to(3,\ 2)}`

Explanation:

`\left\{\begin{array}{ccc}y=3x-7&(1)\\4x+3y=18&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\4x+3(3x-7)=18\qquad\text{use the distributive property}\\\\4x+(3)(3x)+(3)(-7)=18\\\\4x+9x-21=18\qquad\text{add 21 to both sides}\\\\4x+9x-21+21=18+21\qquad\text{cobine like terms}\\\\13x=39\qquad\text{divide both sides by 13}\\\\(13x)/(13)=(39)/(13)\\\\\boxed{x=3}\\\\\text{Substitute it to (1):}\\\\y=3(3)-7\\\\y=9-7\\\\\boxed{y=2}`

Answer 2

x = 3

y = 2

Explanation:

4x + 3(3x - 7) = 18 Substitute y

4x + 9x - 21 = 18 Simply

13x - 21 = 18 Add like terms

13x = 39 Add 21

x = 3 Divide by 13

y = 3(3) - 7 Substitute x

y = 9 - 7 Simply

y = 2 Subtract

Let's check:

4(3) + 3(2) = 18

12 + 6 = 18

18 = 18

It works!