Unit 2, Lesson 13
Solving Systems by Substitution
Algebra 1
Practice
Problem 1
Identify a solution to this system of equations: \(\begin{cases} \text-4x+3y=23 \\ x-y=\text-7 \\ \end{cases}\)
\((\text-5,2)\)
\((\text-2,5)\)
\((\text-3,4)\)
\((4,\text-3)\)
Problem 2
Lin is solving this system of equations: \(\begin{cases} 6x-5y=34 \\ 3x+2y=8 \\ \end{cases}\)
She starts by rearranging the second equation to isolate the \(y\) variable: \(y=4-1.5x\). She then substituted the expression \(4-1.5x\) for \(y\) in the first equation, as shown:
\(\begin{align} 6x-5(4-1.5x) &= 34 \\ 6x-20-7.5x &= 34 \\ \text-1.5x &= 54 \\ x &= \text-36 \\ \end{align} \)
\(\begin{align}y&=4-1.5x\\y &= 4-1.5 \boldcdot (\text-36) \\ y &= 58 \\ \end{align} \)
- Check to see if Lin's solution of \((\text-36,58)\) makes both equations in the system true.
- If your answer to the previous question is "no," find and explain her mistake. If your answer is "yes," graph the equations to verify the solution of the system.