x=-2
y=-1
(-2,-1)
Explanation
Step 1
Let
[tex]\begin{gathered} 5x+4y=-14\text{ Equation(1)} \\ y=-7x-15\text{ Equation(2)} \end{gathered}[/tex]
Step 2
substitute the value of y , form equation (1) in equation(2)
[tex]\begin{gathered} 5x+4y=-14 \\ \text{then} \\ 5x+4(-7x-15)=-14 \end{gathered}[/tex]
Step 3
apply the distributive property to eliminate the parenthesis
[tex]\begin{gathered} 5x+4(-7x-15)=-14 \\ 5x-28x-60=-14 \\ -23x-60=-14 \end{gathered}[/tex]
Step 4
add 60 in both sides
[tex]\begin{gathered} -23x-60=-14 \\ -23x-60+60=-14+60 \\ -23x=46 \end{gathered}[/tex]
Step 5
finally, divide each side by -23
[tex]\begin{gathered} -23x=46 \\ \frac{-23x}{-23}=\frac{46}{-23} \\ x=-2 \end{gathered}[/tex]
Step 6
Finally, replace the value of x=-2 in equation (2) to find y
[tex]\begin{gathered} y=-7x-15 \\ y=-7(-2)-15 \\ y=14-15 \\ y=-1 \end{gathered}[/tex]
so, the answer is (-2,-1)
