Question

How do you use substitution to solve the system of equations 3x - 7= y and 2x + 5y = 16?

How do you use substitution to solve the system of equations 3x - 7= y and 2x + 5y = 16?

Answer 1

See the entire solution process below:

Explanation:

Step 1) Because the first equation is already solved for $y$ we can substitute $3 x - 7$ for $y$ in the second equation and solve for $x$:

$2 x + 5 y = 16$ becomes:

$2 x + 5 \left(3 x - 7\right) = 16$

$2 x + \left(5 \times 3 x\right) - \left(5 \times 7\right) = 16$

$2 x + 15 x - 35 = 16$

$17 x - 35 = 16$

$17 x - 35 + \textcolor{red}{35} = 16 + \textcolor{red}{35}$

$17 x - 0 = 51$

$17 x = 51$

$\frac{17 x}{\textcolor{red}{17}} = \frac{51}{\textcolor{red}{17}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{17}}} x}{\cancel{\textcolor{red}{17}}} = 3$

$x = 3$

Step 2) Substitute $3$ for $x$ in the first equation and calculate $y$:

$3 x - 7 = y$ becomes:

$\left(3 \times 3\right) - 7 = y$

$9 - 7 = y$

$2 = y$

$y = 2$

The solution is: $x = 3$ and $y = 2$ or $\left(3 , 2\right)$

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