Question

Asked Feb 14, 2020

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Solve the system of equations using substitution. Show all of your steps.

5x - 6y = -18

y = 11/6 x + 6

Write your answer as an ordered pair.

Step 1: Here assume 5x - 6y = -18 as equation (1) and assume y = 11/6 x + 6 as equation (2)

5x - 6y = -18 ---(1)

y = 11/6 x + 6 --(2)

Step 2: Now using equations (1) and (2) and using substitution of value of y from equation(2) to (1)

Hence, 5x - 6(11/6 x + 6)=-8

⟹5x-11/x-36=-8

⟹(5x2-11)/x=-8+36

⟹(5x2-11)=28x

⟹5x2-28x-11=0

Now we can use Sridharacharya formula for finding the roots of a quadratic equation ax² + bx + c = 0 , where a is not equal to 0 and a,b, c are real coefficients of the equation.

Being quadratic it has 2 roots.

so ,x ={-b + √(b² - 4ac) } / 2a --(3)

x= {-b-√(b² -4ac)} / 2a----------(4)

here a=5,b=-28 and c=11

so put these values in equation(3) and equation (4) gives

x=5.968 and x=-0.36 now put these two values in eqation (1)

⟹6y=-18-5(5.968)

⟹y=-7.97333 for x=5.968

and 6y=-18-5(-0.36)

⟹y=-2.7 for x=-0.36

hence ordered pairr are

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