Question

is $(-5, -5)$ a solution to the following system of equations?
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$$\begin{cases} y = -2x - 15 \\\\ y = 4x + 15 \\end{cases}$$

Explanation:

Step1: Check first equation

Substitute \( x = -5 \), \( y = -5 \) into \( y = -2x - 15 \).
Right - hand side: \( -2\times(-5)-15=10 - 15=-5 \).
Left - hand side: \( y=-5 \).
Since left - hand side = right - hand side, \((-5,-5)\) satisfies the first equation.

Step2: Check second equation

Substitute \( x = -5 \), \( y = -5 \) into \( y = 4x + 15 \).
Right - hand side: \( 4\times(-5)+15=-20 + 15=-5 \).
Left - hand side: \( y = -5 \).
Since left - hand side = right - hand side, \((-5,-5)\) satisfies the second equation.

Answer:

Yes, \((-5,-5)\) is a solution to the given system of equations.