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

Studdy 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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