Question

determine which of the given points lies on both of the lines in the system of equations by substituting each point into both equations.$\begin{cases}x - y = 7 \\2x + y = 2end{cases}$answer$circ (1,0)$$circ (4,-3)$$circ (-2,6)$$circ (3,-4)$

Explanation:

Step1: Test point (1,0) in Eq1

Substitute $x=1, y=0$ into $x-y=7$:
$1 - 0 = 1
eq 7$ → Fails Eq1.

Step2: Test point (4,-3) in Eq1

Substitute $x=4, y=-3$ into $x-y=7$:
$4 - (-3) = 4 + 3 = 7$ → Passes Eq1.

Step3: Test point (4,-3) in Eq2

Substitute $x=4, y=-3$ into $2x+y=2$:
$2(4) + (-3) = 8 - 3 = 5
eq 2$ → Fails Eq2.

Step4: Test point (-2,6) in Eq1

Substitute $x=-2, y=6$ into $x-y=7$:
$-2 - 6 = -8
eq 7$ → Fails Eq1.

Step5: Test point (3,-4) in Eq1

Substitute $x=3, y=-4$ into $x-y=7$:
$3 - (-4) = 3 + 4 = 7$ → Passes Eq1.

Step6: Test point (3,-4) in Eq2

Substitute $x=3, y=-4$ into $2x+y=2$:
$2(3) + (-4) = 6 - 4 = 2$ → Passes Eq2.

Answer:

○ (3, -4)