Question

Solve the system by substitution. 4x+3y=5x=4y+6

Answer 1

We have a system of simultaneous equations and are required to solve via substitution.

We are simply asked to get x or y in terms of the other and substitute in the other equation to solve for the variable.

When solved, this found variable will be used to solve the other variable.

`\begin{gathered} 4x+3y=5\ldots(1) \\ x=4y+6\ldots(2) \\ \text{ We substitute this value of x in eqn 2 in eqn 1 to get:} \\ 4(4y+6)+3y=5 \\ 16y+24+3y=5 \\ \text{ We subtract 24 from both sides of the equation to get:} \\ 19y=5-24=-19 \\ \text{ We divide both sides of the equation to get:} \\ y=-(19)/(19)=-1 \end{gathered}`

Now we know y, we substitute this value of y into equation 1 to get:

`\begin{gathered} 4x+3(-1)=5 \\ 4x-3=5 \\ \text{ We add 3 to both sides to get:} \\ 4x=5+3=8 \\ \text{ Divide both sides by }4\text{ to get:} \\ x=(8)/(4)=2 \end{gathered}`

x = 2

y =-1