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What is the solution to the system of equations?

y = A system of equations. y equals StartFraction one-third EndFraction minus 10. 2 x plus y equals 4.x – 10

2x + y = 4

(–8, 6)
(–6, 16)
(6, –8)
(16, –6)

Respuesta :

Answer:

Step-by-step explanation:

(6,-8)

Answer : The solution to the system of equations is, (6, -8)

Step-by-step explanation :

As we are given the two equations:

[tex]y=\frac{1}{3}x-10[/tex]     ............(1)

[tex]2x+y=4[/tex]    ..........(2)

Now put equation 1 in equation 2, we get:

[tex]2x+y=4[/tex]

[tex]2x+(\frac{1}{3}x-10)=4[/tex]

[tex]2x+\frac{1}{3}x-10=4[/tex]

[tex]\frac{7}{3}x-10=4[/tex]

[tex]\frac{7}{3}x=4+10[/tex]

[tex]\frac{7}{3}x=14[/tex]

[tex]x=14\times \frac{3}{7}[/tex]

[tex]x=6[/tex]

Now put the value of 'x' in equation 1, we get:

[tex]y=\frac{1}{3}x-10[/tex]

[tex]y=(\frac{1}{3}\times 6)-10[/tex]

[tex]y=2-10[/tex]

[tex]y=-8[/tex]

Thus, the solution to the system of equations is, (6, -8)

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