We can check our answers by substituting the points into both equations. If they produce true statements, our solutions are correct. Let's start by checking

(6, 10) .

We will substitute

6

and

10

for

x

and

y,

respectively, in Equation (I) and Equation (II).

{y = x^{2} - 13 x + 52 y = - 14 x + 94 (I) (II)

$(I), (II):$ $x = 6$ , $y = 10$

{10 = ? 6^{2} - 13 (6) + 52 10 = ? - 14 (6) + 94

▼

Simplify

CalcPow

$(I):$ Calculate power

{10 = ? 36 - 13 (6) + 52 10 = ? - 14 (6) + 94

$(I), (II):$ Multiply

{10 = ? 36 - 78 + 52 10 = ? - 84 + 94

$(I), (II):$ Add and subtract terms

{10 = 10 ✓ 10 = 10 ✓

Since both equations produced true statements, the solution

(6, 10)

is correct. Let's now check

(- 7, 192) .

{y = x^{2} - 13 x + 52 y = - 14 x + 94 (I) (II)

$(I), (II):$ $x = - 7$ , $y = 10$

{192 = ? (- 7)^{2} - 13 (- 7) + 52 192 = ? - 14 (- 7) + 94

▼

Simplify

CalcPow

$(I):$ Calculate power

{192 = ? 49 - 13 (- 7) + 52 192 = ? - 14 (- 7) + 94

$(I), (II):$ $- a (- b) = a \cdot b$

{192 = ? 49 + 91 + 52 192 = ? 98 + 94

$(I), (II):$ Add terms

{192 = 192 ✓ 192 = 192 ✓

Since again both equations produce true statements, the solution

(- 7, 192)

is also correct.

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