Question

Solving Systems by Substitution Day 13x-4y=-5x=y+2Word bank: (5,-2) (5,5) (2,6) NO SOLUTION INFINITE SOLUTIONS (11, 13) (-2,-6) (0,0) (2.-6) (6,2)

Answer 1

hello

we are going to solve this question via substitution method

$\begin{gathered} 3x-4y=-5\ldots\text{equ}1 \\ x=y+2\ldots\text{equ}2 \end{gathered}$

put equation 2 into equation 1

$\begin{gathered} 3x-4y=-5 \\ x=y+2 \\ 3(y+2)-4y=-5 \\ 3y+6-4y=-5 \\ -y+6=-5 \\ -y=-6-5 \\ -y=-11 \\ \text{divide both sides by -1} \\ -\frac{y}{-1}=-\frac{11}{-1} \\ y=11 \end{gathered}$

put y = 11 into equation 1 or 2

with equation 1

put y = 11

$\begin{gathered} 3x-4y=-5 \\ y=11 \\ 3x-4(11)=-5 \\ 3x-44=-5 \\ 3x=-5+44 \\ 3x=39 \\ \text{divide both sides by 3} \\ \frac{3x}{3}=\frac{39}{3} \\ x=13 \end{gathered}$

fro the calculations above, the solutions to the equations with the value of x and y are (13) and (11)