Answered

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Find the solution of the system of equations 3x+4y=10 and x−y=1 . Give the x value followed by the y value, separated by a comma.

Sagot :

Explanation:

The equations are given below as

[tex]\begin{gathered} 3x+4y=10----(1) \\ x-y=1------(2) \end{gathered}[/tex]

From equation (2) make x the subject of the formula

[tex]\begin{gathered} x-y=1 \\ x=1+y-----(3) \end{gathered}[/tex]

Substitute equation (3) in equation (1)

[tex]\begin{gathered} 3x+4y=10 \\ 3(1+y)+4y=10 \\ 3+3y+4y=10 \\ 3+7y=10 \\ collect\text{ similar terms, we will have} \\ 7y=10-3 \\ 7y=7 \\ \frac{7y}{7}=\frac{7}{7} \\ y=1 \end{gathered}[/tex]

Substitute y=1 in equation (3)

[tex]\begin{gathered} x=1+y \\ x=1+1 \\ x=2 \end{gathered}[/tex]

Hence,

Th solution of the system of equations is

[tex](x,y)\Rightarrow(2,1)[/tex]

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