Solved on Nov 05, 2023

Solve the system of linear equations $y=-2.89x+7.07, y=1.56x-7.26$ and select the correct solution.

STEP 1

Assumptions1. We have two linear equations $y=-.89x+7.07$ and $y=1.56x-7.26$ . . We are asked to solve the system using elimination method.
3. The solution will be the point of intersection of these two lines.

STEP 2

In the elimination method, we add or subtract the equations in order to eliminate one of the variables. In this case, since $y$ is already isolated in both equations, we can set the two equations equal to each other to eliminate $y$ .
$-2.89x+7.07 =1.56x-7.26$

STEP 3

Next, we can solve for $x$ by first moving the $-2.89x$ term from the left side of the equation to the right side by adding $2.89x$ to both sides. $7.07 =1.56x +2.89x -7.26$

STEP 4

Combine like terms on the right side of the equation.
$7.07 =4.45x -7.26$

STEP 5

Next, move the $-7.26$ term from the right side of the equation to the left side by adding $7.26$ to both sides. $14.33 =4.45x$

STEP 6

Finally, solve for $x$ by dividing both sides of the equation by $4.45$ .
$x = \frac{14.33}{4.45}$

STEP 7

Calculate the value of $x$ .
$x = \frac{14.33}{4.45} \approx3.22$

STEP 8

Now that we have the value for $x$ , we can substitute it into either of the original equations to find the corresponding value for $y$ . Let's use the first equation $y=-2.89x+7.07$ .
$y = -2.89(3.22) +7.07$

STEP 9

Calculate the value of $y$ .
$y = -2.89(3.22) +7.07 \approx -2.33$

STEP 10

So, the solution to the system of equations is the ordered pair $(x, y)$ , which is approximately $(3.22, -2.33)$ .This means the correct choice is A. The solution is $(3.22, -2.33)$ .
To verify this solution, you can plot the two lines on a graphing calculator and find their point of intersection. The coordinates of the intersection point should match the solution we found.

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Solve the system of linear equations $y=-2.89x+7.07, y=1.56x-7.26$ and select the correct solution.

STEP 1

Assumptions1. We have two linear equations $y=-.89x+7.07$ and $y=1.56x-7.26$ . . We are asked to solve the system using elimination method.
3. The solution will be the point of intersection of these two lines.

STEP 2

In the elimination method, we add or subtract the equations in order to eliminate one of the variables. In this case, since $y$ is already isolated in both equations, we can set the two equations equal to each other to eliminate $y$ .
$-2.89x+7.07 =1.56x-7.26$

STEP 3

Next, we can solve for $x$ by first moving the $-2.89x$ term from the left side of the equation to the right side by adding $2.89x$ to both sides. $7.07 =1.56x +2.89x -7.26$

STEP 4

Combine like terms on the right side of the equation.
$7.07 =4.45x -7.26$

STEP 5

Next, move the $-7.26$ term from the right side of the equation to the left side by adding $7.26$ to both sides. $14.33 =4.45x$

STEP 6

Finally, solve for $x$ by dividing both sides of the equation by $4.45$ .
$x = \frac{14.33}{4.45}$

STEP 7

Calculate the value of $x$ .
$x = \frac{14.33}{4.45} \approx3.22$

STEP 8

Now that we have the value for $x$ , we can substitute it into either of the original equations to find the corresponding value for $y$ . Let's use the first equation $y=-2.89x+7.07$ .
$y = -2.89(3.22) +7.07$

STEP 9

Calculate the value of $y$ .
$y = -2.89(3.22) +7.07 \approx -2.33$

STEP 10

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Solve the system of linear equations y=−2.89x+7.07,y=1.56x−7.26y=-2.89x+7.07, y=1.56x-7.26y=−2.89x+7.07,y=1.56x−7.26 and select the correct solution.

STEP 1

Assumptions1. We have two linear equations y=−.89x+7.07y=-.89x+7.07y=−.89x+7.07 and y=1.56x−7.26y=1.56x-7.26y=1.56x−7.26. . We are asked to solve the system using elimination method.3. The solution will be the point of intersection of these two lines.

STEP 2

STEP 3

Next, we can solve for xxx by first moving the −2.89x-2.89x−2.89x term from the left side of the equation to the right side by adding 2.89x2.89x2.89x to both sides.7.07=1.56x+2.89x−7.267.07 =1.56x +2.89x -7.267.07=1.56x+2.89x−7.26

STEP 4

Combine like terms on the right side of the equation.7.07=4.45x−7.267.07 =4.45x -7.267.07=4.45x−7.26

STEP 5

Next, move the −7.26-7.26−7.26 term from the right side of the equation to the left side by adding 7.267.267.26 to both sides.14.33=4.45x14.33 =4.45x14.33=4.45x

STEP 6

Finally, solve for xxx by dividing both sides of the equation by 4.454.454.45.x=14.334.45x = \frac{14.33}{4.45}x=4.4514.33​

STEP 7

Calculate the value of xxx.x=14.334.45≈3.22x = \frac{14.33}{4.45} \approx3.22x=4.4514.33​≈3.22

STEP 8

Now that we have the value for xxx, we can substitute it into either of the original equations to find the corresponding value for yyy. Let's use the first equation y=−2.89x+7.07y=-2.89x+7.07y=−2.89x+7.07.y=−2.89(3.22)+7.07y = -2.89(3.22) +7.07y=−2.89(3.22)+7.07

STEP 9

Calculate the value of yyy.y=−2.89(3.22)+7.07≈−2.33y = -2.89(3.22) +7.07 \approx -2.33y=−2.89(3.22)+7.07≈−2.33

STEP 10

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

Solve the system of linear equations $y=-2.89x+7.07, y=1.56x-7.26$ and select the correct solution.

Assumptions1. We have two linear equations $y=-.89x+7.07$ and $y=1.56x-7.26$ . . We are asked to solve the system using elimination method.
3. The solution will be the point of intersection of these two lines.

Next, we can solve for $x$ by first moving the $-2.89x$ term from the left side of the equation to the right side by adding $2.89x$ to both sides. $7.07 =1.56x +2.89x -7.26$

Combine like terms on the right side of the equation.
$7.07 =4.45x -7.26$

Next, move the $-7.26$ term from the right side of the equation to the left side by adding $7.26$ to both sides. $14.33 =4.45x$

Finally, solve for $x$ by dividing both sides of the equation by $4.45$ .
$x = \frac{14.33}{4.45}$

Calculate the value of $x$ .
$x = \frac{14.33}{4.45} \approx3.22$

Now that we have the value for $x$ , we can substitute it into either of the original equations to find the corresponding value for $y$ . Let's use the first equation $y=-2.89x+7.07$ .
$y = -2.89(3.22) +7.07$

Calculate the value of $y$ .
$y = -2.89(3.22) +7.07 \approx -2.33$