Solve this system of equations without graphing and show yourreasoning:5x + y = 720x + 2 = y

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04-11-2022
Mathematics

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Solve this system of equations without graphing and show yourreasoning:5x + y = 720x + 2 = y

Sagot :

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KelbyT694623 KelbyT694623 · Answer 1 · 2022-11-04T03:05:53-04:00

We can use substitution method to solve this equation.

Given

5x + y = 7 ---------------------------------------------------------- Equation 1

20x + 2 = y ---------------------------------------------------------- Equation 2

We can substitute Equation 2 into Equation 1, thus, we have:

[tex]\begin{gathered} 5x+y=7 \\ 5x+(20x+2)=7 \\ 5x+20x+2=7 \end{gathered}[/tex]

Now, we have an equation in x. We can do algebra and solve for x. Shown below:

[tex]\begin{gathered} 5x+20x+2=7 \\ 25x=5 \\ x=\frac{5}{25} \\ x=\frac{1}{5} \end{gathered}[/tex]

Now, we use this value of x and substitute into equation 2 to find the value of y. Shown below:

[tex]\begin{gathered} y=20x+2 \\ y=20(\frac{1}{5})+2 \\ y=4+2 \\ y=6 \end{gathered}[/tex]

Final solution:

[tex]x=\frac{1}{5},y=6[/tex]

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