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Math question 4 help

Math question 4 help-example-1
User Moudiz
by
8.3k points

1 Answer

3 votes

Answer:

-1 and 0

Explanation:

This is a set of simultaneous equations. To solve them, you need to substitute one into the other. The easiest way to do this would be to rearrange x - y = -6 to make x the subject:

x = -6 + y

x = y - 6

Now we can substitute this equation into y = -x^2 + 5x + 6:

y = -(y - 6)^2 + 5(y - 6) + 6

Now simplify this equation, and rearrange to make it equal to 0:

y = -y^2 + 12y - 36 + 6

y = -y^2 + 12y - 30

0 = -y^2 + 12y - y - 30

-y^2 + 11y - 30 = 0

Now solve this quadratic equation to obtain two solutions:

y = 5, y = 6

Now substitute these values back into one of the starting equations to find the respective values for x:

When y = 5:

x - 5 = -6

x = -1

When y = 6

x - 6 = -6

x = 0

Therefore, the x solutions are -1 and 0.

User Lienau
by
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