The table can be used to determine the solution to the system of equations, 2y − x = 8, and y − 2x = −5.

A table with 6 columns and 2 rows. The first column, Original System has 2 y minus x equals 8 and y minus 2 x equals negative 5. The second column, Equivalent System, has 2 y minus x equals 8 and negative y plus 4 x equals 10. The third column, Sum of equations in Equivalent System, has 3 x equals 18. The fourth column, Solution to System, is blank. The fifth column, New System Using Sum, has2 y minus x equals 8 and 3 x equals 18. The sixth column, Solution to New System is blank.

Which solution can be used to fill in both blanks in the table?

This are also known as a set of simultaneous equations, also known as a system of equations which is a finite set of equations for which common solutions

Given the following system of equations

2y − x = 8, and

y − 2x = −5.

From equation 2;

y = -5 + 2x ............. 3

Substitute equation 2 into equation 1 to have:

2(-5+2x) - x = 8

Expand to have:

-10 +4x -x = 8

-10 + 3x = 8

3x = 8 + 10

3x = 18

Divide both sides

by 3

3x/3 = 18/3

x = 6

Substitute x = 6 into equation 3

y = -5 + 2x

y = -5 + 2(3)

y = -5 + 6

y = 1

Hence the solution to the system and the solution that fills the blank space is (6, 1)

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