Mathematics
ashleigh5
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Solve the following by substitution : - x + y = 10 x - y = 5

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rishimisra15

Your question is  - x + y = 10 x - y = 5 Now, let us solve this system by the substitution method. According to equation 2 , x - y = 5 thus, x = 5 + y Substituting the value of x in equation 1, (5 + y) + y = 10 5 + 2y = 10 2y = 10 - 5 = 5 thus, y = 5/2 Substituting the value of y in value of x, x = 5 + y = 5 + 5/2 = 15/2 Thus, x = 15/2 ( or 7.5) y = 5/2 ( or 2.5)

Gracie216

[latex]\begin{cases} x + y = 10 \\ x - y = 5 \end{cases}\\ \\ \begin{cases} y = 10 -x\\ x - y = 5 \end{cases}\\ \\ \begin{cases} y = 10 -x\\ x - (10-x) = 5 \end{cases}\\ \\ \begin{cases} y = 10 -x\\ x - 10+x = 5 \end{cases}\\ \\[/latex] [latex]\begin{cases} y = 10 -x\\ 2x - 10 = 5 \end{cases}\\ \\\begin{cases} y = 10 -x\\ 2x = 5 +10 \end{cases}\\ \\ \begin{cases} y = 10 -x\\ 2x =15 \ \ /:2 \end{cases}\\ \\ \begin{cases} y = 10 -x\\ x =\frac{15}{2} \end{cases}\\ \\[/latex] [latex]\begin{cases} y = 10 - 7\frac{1}{2}\\ x =7\frac{1}{2} \end{cases}\\ \\ \begin{cases} y = 2\frac{1}{2}\\ x = 8\frac{1}{2} \end{cases}\\ \\[/latex]  

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