CCSS.HSA.REI.C.7.Q.A1.SQE.15 - Solve the system of equations

Sangeetha Pulapaka (last edited 4 years ago) (Expert, Educator @Qalaxia)

Step 1: Set the equations across each other

x^{2} - 5x + 5 = 5x - 20

x^{2} -10 x +25 = 0

Step 2: Factorise the quadratic and solve for x

Recall how to factorise a quadratic equation

Factorise x^{2} - 10 x +25 = 0

x^{2} - 5x - 5x + 25 = 0

x(x - 5) - 5 ( x - 5) = 0

x = 5, 5

Step 3: Find the value of y

Plugging in the value of x = 5 in y = x^{2} - 5 x + 5

y = 25 - 25 + 5 = 5

So (5,5) is the solution

Skills to know before solving this question

1.What is a quadratic equation

2.What is a linear equation