Question

Solve the system algebraically. 3x - 2y - 1 = 0 y = 5x + 4 What is the solution? {(-9/7,-17/7)} {(9/7,17/7)} {(9/7,-17/7)}

Answer 1

Answer:

$\large\boxed{\left(-\dfrac{9}{7},\ -\dfrac{17}{7}\right)}$

Step-by-step explanation:

$\left\{\begin{array}{ccc}3x-2y-1=0&\text{add 1 to both sides}\\y=5x+4&\text{subtract}\ 5x\ \text{from both sides}\end{array}\right\\\left\{\begin{array}{ccc}3x-2y=1\\-5x+y=4&\text{multiply both sides by 2}\end{array}\right\\\underline{+\\\left\{\begin{array}{ccc}3x-2y=1\\-10x+2y=8\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-7x=9\qquad\text{divide bpth sides by (-7)}\\.\qquad x=-\dfrac{9}{7}\\\\\text{Put it to the second equation:}\\\\y=5\left(-\dfrac{9}{7}\right)+4\\\\y=-\dfrac{45}{7}+\dfrac{28}{7}\\\\y=-\dfrac{17}{7}$

Answer 2

3x - 2y - 1 = 0
y = 5x + 4

3x - 2(5x + 4) - 1 = 0
3x - 10x - 8 - 1 = 0
-7x - 9 = 0
-7x = 9
x = -9/7

y = 5x + 4
y = 5(-9/7) + 4
y = -45/7 + 4
y = -45/7 + 28/7
y = - 17/7

solution is (-9/7, -17/7)