Question

Solve by the elimination method. Check your work.

Answer 1

#1

• 10x-9y=46--(1)
• -2x+3y=10--(2)

(2)×3

`\\ \tt\hookrightarrow -6x+9y=30`--(3)

Subtracting eq(1) from (3)

`\\ \tt\hookrightarrow -16x=-16`

`\\ \tt\hookrightarrow x=1`

Put in eq(2)

`\\ \tt\hookrightarrow -2+3y=10`

`\\ \tt\hookrightarrow y=4`

#2

• 4x+3y=8--(1)
• x-2y=13--(2)

(2) ×4

`\\ \tt\hookrightarrow 4x-8y=52--(3`

Subtracting eq(1) from (3)

`\\ \tt\hookrightarrow -11y=44`

`\\ \tt\hookrightarrow y=-4`

Put in eq(2)

`\\ \tt\hookrightarrow x+8=13`

`\\ \tt\hookrightarrow x=5`

Answer 2

1: x = 19 y = 16 ; 2. x = 5 y = -4

Explanation:

To check your work plug the numbers back into one of the equations and see if it's true.

For example:
10(19)-9(16)=46

46=46

1. I distributed 3 to all the numbers so that 9y and -9y would cancel then you add like terms.

2. I distributed -4 to all the numbers so that 4x and -4x would cancel. Then add all like terms.

Once you get x or y plug it back into one problem to get the other variable.

Hope this helps!