Question

(04.01 LC)

The equations y = −3x + 1 and y = 2x − 4 are shown in the graph.

graph of y equals 2 times x minus 4 and y equals negative 3 times x plus 1

Which is the solution to the system of equations? (1 point)

Group of answer choices

(−2, −1)

(−2, 1)

(−1, −2)

(1, −2)

Answer 1

So, the solution to the system of equations is (1,-2)

To find the solution to the system of equations, you need to find the point where the two equations intersect. This point represents the values of x and y that satisfy both equations simultaneously.

The system of equations is:

y=−3x+1

y=2x−4

To find the solution, set the right-hand sides equal to each other since they both equal y:

−3x+1=2x−4

Now, solve for x:

−3x−2x=−4−1

−5x=−5

Divide by -5 to solve for x:

x=1
Now that you have the value of x, substitute it back into either equation to find the corresponding y. Let's use the first equation:

y=−3(1)+1

y=−3+1

y=−2

So, the solution to the system of equations is (1,-2)

Therefore, the correct answer from the given choices is:(1,−2)

Answer 2

(1, −2)

Explanation:

−3x + 1 = 2x − 4

−5x + 1 = − 4........subtract 2x from both sides

-5x = -5.................subtract 4 from both sides

x = 1.......................divide both sides by - 5

now that you have x value find y by plugging in the x value in either one of the equations (I'll be using y = -3 +1)

y = -3(1)+1

y = -3+1.............multiply

y = -2................add