Question

1. $y = -2x - 7$

$-5x + 2y = 4$
$(-2, 3)$
solution? $square$ yes $square$ no

1. $2x + y = 2$

$-7x - 3y = -5$
$(-1, 4)$
solution? $square$ yes $square$ no
decide whether the given ordered pair is a solution to the system of equations.

1. $y = 4(x + 1) - 5$

$y = -x + 4$
$(5, -1)$
$square$ yes $square$ no

1. $3x - y = -9$

$y = -3(x - 4) - 2$
$(-4, -3)$
$square$ yes $square$ no

Explanation:

Problem 3

Step1: Check first equation

Substitute \(x = -2\), \(y = 3\) into \(y = -2x - 7\).
Right - hand side: \(-2\times(-2)-7=4 - 7=-3\). Left - hand side: \(y = 3\). Since \(3
eq - 3\), we can already say it's not a solution. But let's check the second equation too.

Step2: Check second equation

Substitute \(x=-2\), \(y = 3\) into \(-5x + 2y=4\).
Left - hand side: \(-5\times(-2)+2\times3 = 10 + 6=16
eq4\).

Step1: Check first equation

Substitute \(x=-1\), \(y = 4\) into \(2x + y=2\).
Left - hand side: \(2\times(-1)+4=-2 + 4 = 2\), which equals the right - hand side.

Step2: Check second equation

Substitute \(x=-1\), \(y = 4\) into \(-7x-3y=-5\).
Left - hand side: \(-7\times(-1)-3\times4=7-12=-5\), which equals the right - hand side.

Step1: Check first equation

Substitute \(x = 5\), \(y=-1\) into \(y = 4(x + 1)-5\).
Right - hand side: \(4\times(5 + 1)-5=24-5 = 19\). Left - hand side: \(y=-1\). Since \(-1
eq19\), we can say it's not a solution. But let's check the second equation too.

Step2: Check second equation

Substitute \(x = 5\), \(y=-1\) into \(y=-x + 4\).
Right - hand side: \(-5 + 4=-1\), which equals the left - hand side. But since it fails the first equation, it's not a solution.

Answer:

NO

Problem 4