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General Information
Related Benchmark: MAFS.912.A-REI.3.5
Reporting Category: Algebra: Reasoning with Equations & Inequalities
Type: MS: Multiselect
Difficulty: N/A
Question:

The system begin mathsize 12px style P x plus Q y equals R space end style has the solution (3,-1) where F,G,H,P,Q and R are nonzero real numbers.

size 12px F size 12px x size 12px plus size 12px G size 12px y size 12px equals size 12px H

Select all the systems that are also guaranteed to have the solution (3,-1).

Answer Options:

A.

(P+F)x +(Q+G)y=R+H

Fx+Gy=H

B.

(P+F)x+Qy=R+H
Fx+(G+Q)y=h

C.

Px+Qy=R

(3P+F)x+(3Q+G)y=3H+R

D.

Px+Qy=R

(F-2P)x+(G-2Q)y=H-2R

E.

Px+Qy=R

5Fx+5Gy=5H

Answer Key:
A,D,E