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Solve the system graphically and check the solution. 2x+y=4 and y-2x=6

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Graphing the two given equations, let's first determine their x and y intercepts to easily plot them.

2x + y = 4

At x = 0, At y = 0,

2(0) + y = 4 2x + (0) = 4

0 + y = 4 2x + 0 = 4

y = 4 2x = 4

(0,4) 2x/2 = 4/2

x = 2

(2,0)

y - 2x = 6

At x = 0, At y = 0,

y - 2(0) = 6 (0) - 2x = 6

y - 0 = 6 -2x = 6

y = 6 -2x/-2 = 6/-2

(0,6) x = -3

(-3,0)

Let's now plot the graphs,

It appears that the two graphs intersect at (-1/2, 5). The point of intersection is also the solution.

Let's check using the Substitution Method:

2x + y = 4 (Equation 1)

y - 2x = 6 (Equation 2)

y - 2x = 6

y = 2x + 6 (Substitute to Equation 1)

2x + y = 4

2x + (2x + 6) = 4

2x + 2x + 6 = 4

4x = 4 - 6

4x = -2

4x/4 = -2/4

x = -1/2 or -0.5

Let's determine y,

y - 2x = 6

y - 2(-1/2) = 6

y + 1 = 6

y = 6 - 1

y = 5

Therefore, the solution is -1/2, 5. The answer is correct.

Solve the system graphically and check the solution. 2x+y=4 and y-2x=6-example-1
User Hookenz
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