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Lukas graphed the system of equations shown. 2x + 3y = 2 y = A system of equations. 2 x plus 3 y equals 2. y equals StartFraction one-half EndFraction x plus 3.x + 3 A coordinate grid with 2 lines. The first line passes through the points labeled (negative 2, 2), (0, 0.67) and (1, 0). The second line passes through the points labeled (negative 2, 2) and (0, 3). What is the solution to the system of equations? (–2, 2) (0, 0.67) (0, 3) (1, 0)

Respuesta :

RexyGirl

Answer:

(-2,2)

Step-by-step explanation:

just took the test on edge

MrRoyal

A system of equations is a collection of related equations

The solution to the system of equations is (a) (-2,2)

The system of equations is given as:

[tex]2x + 3y = 2[/tex]

[tex]y = \frac 12x + 3[/tex]

Substitute [tex]y = \frac 12x + 3[/tex] in [tex]2x + 3y = 2[/tex]

[tex]2x + 3y = 2[/tex] becomes

[tex]2x + 3(\frac 12x + 3) = 2[/tex]

Open bracket

[tex]2x + \frac 32x + 9 = 2[/tex]

Multiply through by 2

[tex]4x +3x + 18 = 4[/tex]

[tex]7x + 18 = 4[/tex]

Subtract 18 from both sides

[tex]7x = -14[/tex]

Divide both sides by 7

[tex]x = -2[/tex]

Substitute -2 for x in [tex]y = \frac 12x + 3[/tex]

[tex]y = \frac 12(-2) + 3[/tex]

[tex]y = -1 + 3[/tex]

Add -1 and 3

[tex]y = 2[/tex]

So, we have:

[tex]x = -2[/tex] and [tex]y = 2[/tex]

Express as an ordered pair

[tex](x,y)= (-2,2)[/tex]

Hence, the solution to the system of equations is (a) (-2,2)

Read more about system of equations at:

https://brainly.com/question/14323743

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