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Solve the system of equations by substitution.
3x - 4y = 13
5x + 4y = 11
The solution of the system is x = and y=
(Type integers or simplified fractions.)

Solve the system of equations by substitution 3x 4y 13 5x 4y 11 The solution of the system is x and y Type integers or simplified fractions class=

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DeniseLau
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Answer:

[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]

[tex]x=3,\:y=-1[/tex]

Step-by-step explanation:

[tex]3x - 4y = 13[/tex]

[tex]5x + 4y = 11[/tex]

isolate x for 3x-4y=13

[tex]\mathrm{Subsititute\:}x=\frac{13+4y}{3}[/tex]

[tex]\begin{bmatrix}5\cdot \frac{13+4y}{3}+4y=11\end{bmatrix}[/tex]

[tex]\frac{65+32y}{3}=11[/tex]

now isolate y for [tex]\frac{65+32y}{3}=11[/tex]

[tex]\frac{65+32y}{3}=11[/tex]

[tex]65+32y=33[/tex]

[tex]32y=-32[/tex]

Divide both sides by 32

[tex]\frac{32y}{32}=\frac{-32}{32}[/tex]

[tex]y=-1[/tex]

[tex]\mathrm{For\:}x=\frac{13+4y}{3}[/tex]

[tex]\mathrm{Subsititute\:}y=-1[/tex]

[tex]x=\frac{13+4\left(-1\right)}{3}[/tex]

  [tex]=\frac{13-4\cdot \:1}{3}[/tex]

  [tex]=\frac{9}{3}[/tex]

[tex]\mathrm{Divide\:the\:numbers:}\:\frac{9}{3}=3[/tex]

  [tex]=3[/tex]

[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]

[tex]x=3,\:y=-1[/tex]

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