Questions: Solve the system using the substitution method. x-4y=17 y=5x+10

Solve the system using the substitution method. x-4y=17 y=5x+10
Transcript text: Solve the system using the substitution method. \[ x-4 y=17 \] \[ y=5 x+10 \]
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Solution

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Solution Steps

To solve the system of equations using the substitution method, we first solve one of the equations for one variable and then substitute that expression into the other equation. In this case, the second equation is already solved for \( y \). We substitute \( y = 5x + 10 \) into the first equation and solve for \( x \). Once we have the value of \( x \), we substitute it back into the expression for \( y \) to find the value of \( y \).

Step 1: Substitute and Solve for \( x \)

We start with the system of equations: \[ x - 4y = 17 \quad (1) \] \[ y = 5x + 10 \quad (2) \] Substituting equation (2) into equation (1): \[ x - 4(5x + 10) = 17 \] This simplifies to: \[ x - 20x - 40 = 17 \] Combining like terms gives: \[ -19x - 40 = 17 \] Adding 40 to both sides results in: \[ -19x = 57 \] Dividing by -19 yields: \[ x = -3 \]

Step 2: Substitute \( x \) back to find \( y \)

Now that we have \( x = -3 \), we substitute this value back into equation (2): \[ y = 5(-3) + 10 \] Calculating this gives: \[ y = -15 + 10 = -5 \]

Final Answer

The solution to the system of equations is: \[ \boxed{x = -3} \] \[ \boxed{y = -5} \]

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