Question

fill in the value that will make each ordered pair a solution for the given equation.

1. $x + y = 6$

a. $(2, \quad )$
b. $(0, \quad )$
c. $(\quad , 0)$

1. $2x + 4y = 8$

a. $(2, \quad )$
b. $(0, \quad )$
c. $(\quad , 0)$

Explanation:

For Equation 4: $x + y = 6$

Step1: Solve for $y$ when $x=2$

Substitute $x=2$ into $x+y=6$:
$2 + y = 6$
$y = 6 - 2 = 4$

Step2: Solve for $y$ when $x=0$

Substitute $x=0$ into $x+y=6$:
$0 + y = 6$
$y = 6$

Step3: Solve for $x$ when $y=0$

Substitute $y=0$ into $x+y=6$:
$x + 0 = 6$
$x = 6$

For Equation 5: $2x + 4y = 8$

Step4: Solve for $y$ when $x=2$

Substitute $x=2$ into $2x+4y=8$:
$2(2) + 4y = 8$
$4 + 4y = 8$
$4y = 8 - 4 = 4$
$y = \frac{4}{4} = 1$

Step5: Solve for $y$ when $x=0$

Substitute $x=0$ into $2x+4y=8$:
$2(0) + 4y = 8$
$4y = 8$
$y = \frac{8}{4} = 2$

Step6: Solve for $x$ when $y=0$

Substitute $y=0$ into $2x+4y=8$:
$2x + 4(0) = 8$
$2x = 8$
$x = \frac{8}{2} = 4$

Answer:

For $x+y=6$:

a. $(2, 4)$
b. $(0, 6)$
c. $(6, 0)$

For $2x+4y=8$:

a. $(2, 1)$
b. $(0, 2)$
c. $(4, 0)$