Question

Please help with this question. Thank you!!!

Answer 1

Answer:

M(-3, -2.5) and N(3, -1)

Step-by-step explanation:

Given equations:

1st

• 4y = x - 7

make x subject

• x = 4y + 7 ___ equation 1

2nd

• x² + xy = 4 + 2y²

Substitute equation 1 into 2

x² + xy = 4 + 2y²

$\sf step : \ x = 4y + 7$

(4y + 7)² + (4y + 7)y = 4 + 2y²

$\sf step : \ distribute \ inside \ parenthesis$

16y² + 56y + 49 + 4y² + 7y = 4 + 2y²

$\sf step : \ collect \ terms$

16y² + 4y² -2y² + 56y + 7y + 49 - 4 = 0

$\sf step : \ simplify$

18y² + 63y  + 45 = 0

$\sf step : \ middle \ term \ factor$

18y² + 18y + 45y + 45 = 0

$\sf step : \ factor \ out$

18y(y + 1) + 45(y + 1) = 0

$\sf step : \ collect \ into \ groups$

(18y + 45)(y + 1) = 0

$\sf step : \ set \ to \ zero$

y = -2.5, -1

Now, find value of x

x = 4y + 7

when y = -2.5, x = 4(-2.5) + 7 = -3

when y = -1, x = 4(-1) + 7 = 3

Hence the coordinates are (x, y) = M(-3, -2.5) and N(3, -1).