Question

svlc algebra 1a - standard (15260)
solving systems of linear equations: graphing

how many solutions does this linear system have?

y = -6x + 2
-12x - 2y = -4

one solution: (0, 0)
one solution: (1, -4)
infinite number of solutions

no solution

?retest \tmark and return \t8 of 10 \tsave & exit

Explanation:

Step1: Simplify the second equation

Start with the second equation \(-12x - 2y = -4\). Divide every term by \(-2\) to simplify:
\(\frac{-12x}{-2}+\frac{-2y}{-2}=\frac{-4}{-2}\)
Which simplifies to \(6x + y = 2\). Then, solve for \(y\): \(y=-6x + 2\).

Step2: Compare the two equations

The first equation is \(y = -6x + 2\), and the simplified second equation is also \(y=-6x + 2\). This means the two linear equations are identical (they represent the same line).

Answer:

infinite number of solutions