Math / Algebra

Question $\begin{array}{c} x+2 y=7 \\ 2 x+3 y=11 \end{array}$
Which ordered pair $(x, y)$ satisfies the system f equations above? A) $(1,-3)$ 3) $(1,3)$ C) $(-1,3)$ ) $(-1,-3)$

Studdy Solution

STEP 1

What is this asking? We need to find the values of $x$ and $y$ that make both equations true at the same time! Watch out! Don't mix up $x$ and $y$ when plugging the values back into the equations.
Also, make sure your arithmetic is on point!

STEP 2

1. Solve for $x$ using the first equation.
2. Substitute $x$ into the second equation and solve for $y$ .
3. Substitute the value of $y$ back into the equation for $x$ .
4. Check the solution.

STEP 3

We're given $x + 2y = 7$ .
To isolate $x$ , we need to move the $2y$ to the other side of the equation.
We can do this by subtracting $2y$ from both sides of the equation: $x + 2y - 2y = 7 - 2y$ $x = 7 - 2y$ Now we have an expression for $x$ in terms of $y$ !

STEP 4

Our second equation is $2x + 3y = 11$ .
Let's substitute the expression we just found for $x$ into this equation: $2(7 - 2y) + 3y = 11$

STEP 5

Now we distribute the $2$ : $14 - 4y + 3y = 11$ Combine the $y$ terms: $14 - y = 11$ To isolate $y$ , subtract $14$ from both sides: $14 - y - 14 = 11 - 14$ $-y = -3$ Finally, multiply both sides by $-1$ to get: $y = \mathbf{3}$ Awesome! We found the value of $y$ !

STEP 6

Remember our equation for $x$ ?
It was $x = 7 - 2y$ .
Now that we know $y = \mathbf{3}$ , we can substitute it back in: $x = 7 - 2 \cdot \mathbf{3}$ $x = 7 - 6$ $x = \mathbf{1}$ We've got our $x$ value!

STEP 7

Let's check if our solution $x = \mathbf{1}$ and $y = \mathbf{3}$ works in both original equations.
First equation: $\mathbf{1} + 2 \cdot \mathbf{3} = \mathbf{1} + 6 = 7$ , which is correct!
Second equation: $2 \cdot \mathbf{1} + 3 \cdot \mathbf{3} = 2 + 9 = 11$ , which is also correct!

STEP 8

The ordered pair that satisfies the system of equations is $(1, 3)$ , which is answer choice B!

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Question $\begin{array}{c} x+2 y=7 \\ 2 x+3 y=11 \end{array}$
Which ordered pair $(x, y)$ satisfies the system f equations above? A) $(1,-3)$ 3) $(1,3)$ C) $(-1,3)$ ) $(-1,-3)$

Studdy Solution

STEP 1

What is this asking? We need to find the values of $x$ and $y$ that make both equations true at the same time! Watch out! Don't mix up $x$ and $y$ when plugging the values back into the equations.
Also, make sure your arithmetic is on point!

STEP 2

1. Solve for $x$ using the first equation.
2. Substitute $x$ into the second equation and solve for $y$ .
3. Substitute the value of $y$ back into the equation for $x$ .
4. Check the solution.

STEP 3

We're given $x + 2y = 7$ .
To isolate $x$ , we need to move the $2y$ to the other side of the equation.
We can do this by subtracting $2y$ from both sides of the equation: $x + 2y - 2y = 7 - 2y$ $x = 7 - 2y$ Now we have an expression for $x$ in terms of $y$ !

STEP 4

Our second equation is $2x + 3y = 11$ .
Let's substitute the expression we just found for $x$ into this equation: $2(7 - 2y) + 3y = 11$

STEP 5

Now we distribute the $2$ : $14 - 4y + 3y = 11$ Combine the $y$ terms: $14 - y = 11$ To isolate $y$ , subtract $14$ from both sides: $14 - y - 14 = 11 - 14$ $-y = -3$ Finally, multiply both sides by $-1$ to get: $y = \mathbf{3}$ Awesome! We found the value of $y$ !

STEP 6

Remember our equation for $x$ ?
It was $x = 7 - 2y$ .
Now that we know $y = \mathbf{3}$ , we can substitute it back in: $x = 7 - 2 \cdot \mathbf{3}$ $x = 7 - 6$ $x = \mathbf{1}$ We've got our $x$ value!

STEP 7

Let's check if our solution $x = \mathbf{1}$ and $y = \mathbf{3}$ works in both original equations.
First equation: $\mathbf{1} + 2 \cdot \mathbf{3} = \mathbf{1} + 6 = 7$ , which is correct!
Second equation: $2 \cdot \mathbf{1} + 3 \cdot \mathbf{3} = 2 + 9 = 11$ , which is also correct!

STEP 8

The ordered pair that satisfies the system of equations is $(1, 3)$ , which is answer choice B!

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Questionx+2y=72x+3y=11\begin{array}{c} x+2 y=7 \\ 2 x+3 y=11 \end{array}x+2y=72x+3y=11​Which ordered pair (x,y)(x, y)(x,y) satisfies the system f equations above? A) (1,−3)(1,-3)(1,−3) 3) (1,3)(1,3)(1,3) C) (−1,3)(-1,3)(−1,3) ) (−1,−3)(-1,-3)(−1,−3)

Studdy Solution

STEP 1

What is this asking? We need to find the values of xxx and yyy that make both equations true at the same time! Watch out! Don't mix up xxx and yyy when plugging the values back into the equations.Also, make sure your arithmetic is on point!

STEP 2

1. Solve for xxx using the first equation.2. Substitute xxx into the second equation and solve for yyy.3. Substitute the value of yyy back into the equation for xxx.4. Check the solution.

STEP 3

STEP 4

Our second equation is 2x+3y=112x + 3y = 112x+3y=11.Let's **substitute** the expression we just found for xxx into this equation: 2(7−2y)+3y=112(7 - 2y) + 3y = 112(7−2y)+3y=11

STEP 5

STEP 6

Remember our equation for xxx?It was x=7−2yx = 7 - 2yx=7−2y.Now that we know y=3y = \mathbf{3}y=3, we can **substitute** it back in: x=7−2⋅3x = 7 - 2 \cdot \mathbf{3}x=7−2⋅3 x=7−6x = 7 - 6x=7−6x=1x = \mathbf{1}x=1We've got our xxx value!

STEP 7

STEP 8

The ordered pair that satisfies the system of equations is (1,3)(1, 3)(1,3), which is answer choice B!

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question $\begin{array}{c} x+2 y=7 \\ 2 x+3 y=11 \end{array}$
Which ordered pair $(x, y)$ satisfies the system f equations above? A) $(1,-3)$ 3) $(1,3)$ C) $(-1,3)$ ) $(-1,-3)$

What is this asking? We need to find the values of $x$ and $y$ that make both equations true at the same time! Watch out! Don't mix up $x$ and $y$ when plugging the values back into the equations.
Also, make sure your arithmetic is on point!

1. Solve for $x$ using the first equation.
2. Substitute $x$ into the second equation and solve for $y$ .
3. Substitute the value of $y$ back into the equation for $x$ .
4. Check the solution.

Our second equation is $2x + 3y = 11$ .
Let's substitute the expression we just found for $x$ into this equation: $2(7 - 2y) + 3y = 11$

Remember our equation for $x$ ?
It was $x = 7 - 2y$ .
Now that we know $y = \mathbf{3}$ , we can substitute it back in: $x = 7 - 2 \cdot \mathbf{3}$ $x = 7 - 6$ $x = \mathbf{1}$ We've got our $x$ value!

The ordered pair that satisfies the system of equations is $(1, 3)$ , which is answer choice B!