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Math  /  Algebra

QuestionEstimate the solution to the system of equations. Yu con use the interactive groph below to find the solution. {y=−x+2y=3x−4\left\{\begin{array}{l} y=-x+2 \\ y=3 x-4 \end{array}\right.
Choose 1 arower: (A) x=12,y=52x=\frac{1}{2}, y=\frac{5}{2} (D) x=12,y=32x=\frac{1}{2}, y=\frac{3}{2} (c) x=52,y=12x=\frac{5}{2}, y=\frac{1}{2} (C) x=32,y=12x=\frac{3}{2}, y=\frac{1}{2}

Studdy Solution

STEP 1

1. We are given a system of linear equations and need to find the intersection point.
2. The intersection point will satisfy both equations simultaneously.
3. We are estimating the solution, likely by solving algebraically since no graph is provided.

STEP 2

1. Set the equations equal to each other to find the x-coordinate of the intersection.
2. Substitute the x-coordinate back into one of the original equations to find the y-coordinate.
3. Compare the calculated solution to the given options.

STEP 3

Set the two equations equal to each other to find the x-coordinate:
−x+2=3x−4 -x + 2 = 3x - 4

STEP 4

Solve for x x :
Add x x to both sides:
2=4x−4 2 = 4x - 4
Add 4 to both sides:
6=4x 6 = 4x
Divide both sides by 4:
x=32 x = \frac{3}{2}

STEP 5

Substitute x=32 x = \frac{3}{2} into one of the original equations to find y y . Let's use y=−x+2 y = -x + 2 :
y=−(32)+2 y = -\left(\frac{3}{2}\right) + 2
y=−32+2 y = -\frac{3}{2} + 2
Convert 2 to a fraction with a common denominator:
y=−32+42 y = -\frac{3}{2} + \frac{4}{2}
y=12 y = \frac{1}{2}

STEP 6

The solution to the system is x=32,y=12 x = \frac{3}{2}, y = \frac{1}{2} .
Compare this solution to the given options:
The correct answer is (C) x=32,y=12 x = \frac{3}{2}, y = \frac{1}{2} .

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