Question

I need help with number 5Systems of equations by subtracting

Answer 1

Given

We have the equations:

`\begin{gathered} 4x\text{ + 7y = 19} \\ y\text{ = x + 9} \end{gathered}`

Solving simultaneously using substitution method

From equation 2:

`y\text{ = x+ 9}`

Substituting the expression for y into equation (1):

`\begin{gathered} 4x\text{ + 7y = 19} \\ 4x\text{ + 7\lparen x + 9\rparen = 19} \end{gathered}`

Next, we solve for x:

`\begin{gathered} 4x\text{ + 7x + 63 = 19} \\ Collect\text{ like terms} \\ 11x\text{ = -44} \\ x\text{ = -4} \end{gathered}`

Substituting the value of x:

`\begin{gathered} y\text{ = x + 9} \\ =\text{ -4 + 9} \\ =\text{ 5} \end{gathered}`

Answer:

x = -4, y = -5