x 2x -2y = 6

Question

x 2x -2y = 6
3x + 2y = 9
Solve the system of equations.

Ax A x=0, y =3

x B x=3, y= 0

•x C x=1,y=-2

1x D x=-2, y= 1
-×

x= 6, y = 3

GPT-4o mini · Answer

To solve the system of equations: 1. $ 2x - 2y = 6 $ 2. $ 3x + 2y = 9 $ Let's solve it step by step. **Step 1:** Simplify the first equation. Divide the first equation by 2: $$ x - y = 3 \quad \text{(Equation 1)} $$ **Step 2:** Rearrange Equation 1 to express $y$ in terms of $x$: $$ y = x - 3 \quad \text{(Equation 2)} $$ **Step 3:** Substitute Equation 2 into the second equation: Substituting for $y$ in Equation 2: $$ 3x + 2(x - 3) = 9 $$ Simplifying this gives: $$ 3x + 2x - 6 = 9 $$ Combine like terms: $$ 5x - 6 = 9 $$ Add 6 to both sides: $$ 5x = 15 $$ Divide by 5: $$ x = 3 \quad \text{(Value of x)} $$ **Step 4:** Now substitute $x = 3$ back into Equation 2 to find $y$: $$ y = 3 - 3 = 0 \quad \text{(Value of y)} $$ **Final Solution:** The solution to the system of equations is $x = 3$ and $y = 0$. Thus, the answer is: **B**: $x = 3, y = 0$.

AYD3N · Answer

4x 5x + 5y = 140 3x + 9y = 162 What is the solution for the system of equations above? A ✕ =12,y=16 《× B x = 16, y = 12 《× C x =13, y = 15 《× x=15, y = 13

GPT-4o mini · Answer

To solve the system of equations: 1. $ 5x + 5y = 140 $ 2. $ 3x + 9y = 162 $ Let's solve it step by step. **Step 1:** Simplify the first equation. Divide the entire first equation by 5: $$ x + y = 28 \quad \text{(Equation 1)} $$ **Step 2:** Rearrange Equation 1 to express $y$ in terms of $x$: $$ y = 28 - x \quad \text{(Equation 2)} $$ **Step 3:** Substitute Equation 2 into the second equation: Now, substitute for $y$ in the second equation: $$ 3x + 9(28 - x) = 162 $$ Distributing $9$: $$ 3x + 252 - 9x = 162 $$ Combine like terms: $$ -6x + 252 = 162 $$ Subtract 252 from both sides: $$ -6x = 162 - 252 $$ $$ -6x = -90 $$ Divide by -6: $$ x = 15 \quad \text{(Value of x)} $$ **Step 4:** Now substitute $x = 15$ back into Equation 2 to find $y$: $$ y = 28 - 15 = 13 \quad \text{(Value of y)} $$ **Final Solution:** The solution to the system of equations is $x = 15$ and $y = 13$. Thus, the answer is: **D**: $x = 15, y = 13$.

AYD3N · Answer

× 6x + 3y = 9 2x + 3y = 1 Solve the system of equations. 4x A x=2, y=-1 x B x=-1, y =2 C 1 X= -1/2, y=3 D x = 3, y=_1 1x E x=1, y= 1

GPT-4o mini · Answer

To solve the system of equations: 1. $ 6x + 3y = 9 $ 2. $ 2x + 3y = 1 $ Let's solve it step by step. **Step 1:** Simplify the first equation. Divide the entire first equation by 3: $$ 2x + y = 3 \quad \text{(Equation 1)} $$ The second equation remains as is: $$ 2x + 3y = 1 \quad \text{(Equation 2)} $$ **Step 2:** Now we have the system: 1. $ 2x + y = 3 $ (Equation 1) 2. $ 2x + 3y = 1 $ (Equation 2) **Step 3:** Subtract Equation 1 from Equation 2 to eliminate $2x$: $$ (2x + 3y) - (2x + y) = 1 - 3 $$ This simplifies to: $$ 2y = -2 $$ Dividing both sides by 2 gives: $$ y = -1 $$ **Step 4:** Substitute $y = -1$ back into Equation 1 to find $x$: $$ 2x + (-1) = 3 $$ This simplifies to: $$ 2x - 1 = 3 $$ Adding 1 to both sides gives: $$ 2x = 4 $$ Dividing by 2 gives: $$ x = 2 $$ **Final Solution:** The solution to the system of equations is $x = 2$ and $y = -1$. Thus, the answer is: **: $x = 2, y = -1$.

AYD3N · Answer

1× 4x+7y=-33 7x-3y =49 What is the solution for the system of equations above? _x A x = 4, y = -7 B X=-4，ソニー7 X C X=3,y=-7 D x= -3, y = 7

GPT-4o mini · Answer

To solve the system of equations: 1. $ 4x + 7y = -33 $ 2. $ 7x - 3y = 49 $ Let's solve it step by step. **Step 1:** We'll use the elimination method. First, we can eliminate one variable by manipulating the equations. Let's solve for $y$ from the first equation. From the first equation: $$ 7y = -33 - 4x \quad \text{(Equation 1)} $$ This gives: $$ y = \frac{-33 - 4x}{7} \quad \text{(Equation 2)} $$ **Step 2:** Substitute Equation 2 for $y$ in the second equation: $$ 7x - 3\left(\frac{-33 - 4x}{7}\right) = 49 $$ Multiply through by 7 to eliminate the fraction: $$ 49x + 3(33 + 4x) = 343 $$ This simplifies to: $$ 49x + 99 + 12x = 343 $$ Combine like terms: $$ 61x + 99 = 343 $$ **Step 3:** Subtract 99 from both sides: $$ 61x = 244 $$ Now, divide by 61: $$ x = \frac{244}{61} = 4 $$ **Step 4:** Substitute $x = 4$ back into Equation 1 to find $y$: $$ 4(4) + 7y = -33 $$ $$ 16 + 7y = -33 $$ $$ 7y = -33 - 16 $$ $$ 7y = -49 $$ Now divide by 7: $$ y = -7 $$ **Final Solution:** The solution to the system of equations is $x = 4$ and $y = -7$. Thus, the answer is: **: $x = 4, y = -7$.

AYD3N · Answer

1× 9х + 3y=-27 3x + 14y=-48 What is the solution for the system of equations above? A x=4, y=-3 X=-2,y=-4 x=2, y= 3 xD X=-2，ノ=-3

GPT-4o mini · Answer

To solve the system of equations: 1. $ 9x + 3y = -27 $ 2. $ 3x + 14y = -48 $ Let's solve it step by step. **Step 1:** Simplify the first equation. We can divide the entire first equation by 3: $$ 3x + y = -9 \quad \text{(Equation 1)} $$ The second equation remains unchanged: $$ 3x + 14y = -48 \quad \text{(Equation 2)} $$ **Step 2:** Now we have the system: 1. $ 3x + y = -9 $ 2. $ 3x + 14y = -48 $ **Step 3:** We can subtract Equation 1 from Equation 2: $$ (3x + 14y) - (3x + y) = -48 - (-9) $$ This simplifies to: $$ 14y - y = -48 + 9 $$ Combine like terms: $$ 13y = -39 $$ Dividing by 13: $$ y = -3 \quad \text{(Value of y)} $$ **Step 4:** Substitute $y = -3$ back into Equation 1 to find $x$: $$ 3x + (-3) = -9 $$ This simplifies to: $$ 3x - 3 = -9 $$ Adding 3 to both sides yields: $$ 3x = -6 $$ Dividing by 3 gives: $$ x = -2 \quad \text{(Value of x)} $$ **Final Solution:** The solution to the system of equations is $x = -2$ and $y = -3$. Thus, the answer is: **D**: $x = -2, y = -3$.

AYD3N · Answer

1× 3x-y=4 x + 2y = 6 Solve the system of equations. (-2,-2) (2,-2) (2.5,1.75) 』x (2.5,4.75) (2,2)

GPT-4o mini · Answer

To solve the system of equations: 1. $ 3x - y = 4 $ 2. $ x + 2y = 6 $ Let's solve it step by step. **Step 1:** We can rearrange the first equation to express $y$ in terms of $x$: From the first equation: $$ y = 3x - 4 \quad \text{(Equation 1)} $$ **Step 2:** Now substitute Equation 1 into the second equation: Using $y = 3x - 4$ in the second equation $x + 2y = 6$: $$ x + 2(3x - 4) = 6 $$ **Step 3:** Distribute the $2$: $$ x + 6x - 8 = 6 $$ Combine like terms: $$ 7x - 8 = 6 $$ **Step 4:** Add $8$ to both sides: $$ 7x = 14 $$ **Step 5:** Divide by $7$: $$ x = 2 $$ **Step 6:** Substitute $x = 2$ back into Equation 1 to find $y$: $$ y = 3(2) - 4 = 6 - 4 = 2 $$ **Final Solution:** The solution to the system of equations is $x = 2$ and $y = 2$. Thus, the answer is: **(2, 2)**.