QuestionJuly 15, 2025

Use substitution to solve the system. x-3y=16 3x-4y=23 x= square y= square

Use substitution to solve the system. x-3y=16 3x-4y=23 x= square y= square
Use substitution to solve the system.
x-3y=16
3x-4y=23
x= square 
y= square

Solution
4.2(277 votes)

Answer

x = 1 ### y = -5 Explanation 1. Solve for x in terms of y From the first equation, x - 3y = 16, solve for x: x = 3y + 16. 2. Substitute x in the second equation Substitute x = 3y + 16 into 3x - 4y = 23: 3(3y + 16) - 4y = 23. 3. Simplify and solve for y Expand and simplify: 9y + 48 - 4y = 23. Combine like terms: 5y + 48 = 23. Solve for y: 5y = 23 - 48 \Rightarrow 5y = -25 \Rightarrow y = -5. 4. Substitute y back to find x Substitute y = -5 into x = 3y + 16: x = 3(-5) + 16 = -15 + 16 = 1.

Explanation

1. Solve for $x$ in terms of $y$<br /> From the first equation, $x - 3y = 16$, solve for $x$: $x = 3y + 16$.<br /><br />2. Substitute $x$ in the second equation<br /> Substitute $x = 3y + 16$ into $3x - 4y = 23$: <br /> $3(3y + 16) - 4y = 23$.<br /><br />3. Simplify and solve for $y$<br /> Expand and simplify: $9y + 48 - 4y = 23$.<br /> Combine like terms: $5y + 48 = 23$.<br /> Solve for $y$: $5y = 23 - 48 \Rightarrow 5y = -25 \Rightarrow y = -5$.<br /><br />4. Substitute $y$ back to find $x$<br /> Substitute $y = -5$ into $x = 3y + 16$: <br /> $x = 3(-5) + 16 = -15 + 16 = 1$.
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