Question

solve the following system of linear equations by graphing: -2x + 2y=-16 -7x + 7y=-56 graph the linear equations by writing the equations in slope - intercept form: y = x+ y = x+ identify the appropriate number of solutions. if there is a solution, give the point. consistent ( )

Explanation:

Step1: Rewrite first equation in slope - intercept form

Starting with \(-7x + 7y=-56\), add \(7x\) to both sides: \(7y=7x - 56\). Then divide by 7: \(y = x-8\).

Step2: Rewrite second equation in slope - intercept form

Starting with \(-2x + 2y=-16\), add \(2x\) to both sides: \(2y=2x - 16\). Then divide by 2: \(y=x - 8\).

Step3: Analyze the system

Since both equations are the same (\(y=x - 8\)), the lines are identical. So there are infinitely many solutions.

Answer:

Infinitely many solutions; \(y=x - 8\), \(y=x - 8\)