Question

Solve the system by substitution.y = 2x + 4- 3x + 6y = 15

Answer 1

Solve the system of equations by substitution;

`\begin{gathered} y=2x+4---(1) \\ -3x+6y=15---(2) \end{gathered}`

From equation (1), we note that y equals 2x plus 4, hence we substitute this value of y into equation (2)

`\begin{gathered} -3x+6y=15 \\ -3x+6(2x+4)=15 \end{gathered}`

Next, we expand the parenthesis on the left side of the equation

`-3x+12x+24=15`

Next we collect all like terms as follows;

`12x-3x=15-24`

Solve this and we arrive at;

`9x=-9`

Divide both sides by 9

`\begin{gathered} (9x)/(9)=-(-9)/(9) \\ x=-1 \end{gathered}`

We can now substitute for x = -1 into equation (1)

`\begin{gathered} y=2x+4 \\ y=2(-1)+4 \\ y=-2+4 \\ y=4-2 \\ y=2 \end{gathered}`

The solution is

x = -1, y= 2