[4x+8y=20], [-4x+2y=-30] Consider the given system of equations. How many (x,y) solutions does this system have? Choose 1 answer: (A) No solutions (B) Exactly one solution (C) Infinitely many solutions (D) None of the above

Add Equations Together: We have the system of equations: 1) 4x + 8y = 20 2) -4x + 2y = -30 To solve the system, we can add the two equations together to eliminate x.Solve for y: Adding the equations 1) and 2) together: (4x + 8y) + (-4x + 2y) = 20 + (-30) This simplifies to: 4x - 4x + 8y + 2y = 20 - 30 0x + 10y = -10Substitute y into Equation: Now we can solve for y by dividing both sides of the equation by 10: 10y = -10 y = -10 / 10 y = -1Solve for x: With the value of y found, we can substitute it back into one of the original equations to find x. We'll use equation 1): 4x + 8y = 20 Substituting y = -1: 4x + 8(-1) = 20Solving for x: 4x - 8 = 20 Add 8 to both sides: 4x = 20 + 8 4x = 28 Divide both sides by 4: x = 28 / 4 x = 7

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$4x+8y=20$ $\newline$ $-4x+2y=-30$ $\newline$ Consider the given system of equations. How many $(x,y)$ solutions does this system have? $\newline$ Choose $1$ answer: $\newline$ (A) No solutions $\newline$ (B) Exactly one solution $\newline$ (C) Infinitely many solutions $\newline$ (D) None of the above

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Math Problems

Grade 8

Solve a system of equations using any method

Full solution

4x+8y=20

\newline

-4x+2y=-30

\newline

Consider the given system of equations. How many

(x,y)

solutions does this system have?

\newline

Choose

1

answer:

\newline

(A) No solutions

\newline

(B) Exactly one solution

\newline

\newline

(D) None of the above

Add Equations Together: We have the system of equations: $\newline$ $1$ ) $4x + 8y = 20$ $\newline$ $2$ ) $-4x + 2y = -30$ $\newline$ To solve the system, we can add the two equations together to eliminate $x$ .
Solve for y: Adding the equations $1$ ) and $2$ ) together: $\newline$ $(4x + 8y) + (-4x + 2y) = 20 + (-30)$ $\newline$ This simplifies to: $\newline$ $4x - 4x + 8y + 2y = 20 - 30$ $\newline$ $0x + 10y = -10$
Substitute $y$ into Equation: Now we can solve for $y$ by dividing both sides of the equation by $10$ : $10y = -10$ $y = -10 / 10$ $y = -1$
Solve for x: With the value of $y$ found, we can substitute it back into one of the original equations to find $x$ . We'll use equation $1$ ):
$4x + 8y = 20$
Substituting $y = -1$ :
$4x + 8(-1) = 20$
Solve for x: With the value of $y$ found, we can substitute it back into one of the original equations to find $x$ . We'll use equation $1$ ):
$4x + 8y = 20$
Substituting $y = -1$ :
$4x + 8(-1) = 20$ Solving for $x$ :
$4x - 8 = 20$
Add $8$ to both sides:
$4x = 20 + 8$
$4x = 28$
Divide both sides by $x$ $0$ :
$x$ $1$
$x$ $2$