Question

What is the solution to this set of equations? show your work. y=5x-9 y=x^2-3x+7

Answer 1

Answer:

MsEHolt Brainly Teacher

The y-coordinate of the solution is 11.

Both equations have y isolated.  We will use substitution for this system:

5x-9=x²-3x+7

We want to gather all of the variables on one side, so we will subtract 5x from each side:

5x-9-5x=x²-3x+7-5x

-9=x²-8x+7

We want the equation to be equal to 0 to solve it, so we will add 9 to both sides:

-9+9=x²-8x+7+9

0=x²-8x+16

This is easy to factor; factors of 16 that sum to -8 are -4 and -4:

0=(x-4)(x-4)

Since these are the same factor, we solve it to get our answer:

x-4=0

x-4+4=0+4

x=4

Substitute this into the first, linear, equation:

y=5(4)-9=20-9=11

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Step-by-step explanation:

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Answer 2

Answer:

(4, 11)

Step-by-step explanation:

Given the 2 equations

y = 5x - 9 → (1)

y = x² - 3x + 7 → (2)

Substitute y = x² - 3x + 7 into (1)

x² - 3x + 7 = 5x - 9 ( subtract 5x - 9 from both sides )

x² - 8x + 16 = 0 ← in standard form

(x - 4)² = 0 ← in factored form

x - 4 = 0 ⇒ x = 4

Substitute x = 4 into (1) for corresponding value of y

y = (5 × 4) - 9 = 20 - 9 = 11

Solution is (4, 11)