Question

linear equations practice — ordered pairs
directions: each equation represents a line. one, two, or all three of the ordered pairs may
be solutions. check all ordered pairs that satisfy the equation.

1. ( y = 2x )

a. ( (1, 2) ) b. ( (2, 4) ) c. ( (3, 5) )

1. ( y = x + 1 )

a. ( (0, 1) ) b. ( (2, 3) ) c. ( (3, 5) )

1. ( x + y = 6 )

a. ( (2, 4) ) b. ( (3, 3) ) c. ( (1, 5) )

1. ( y = -x + 4 )

a. ( (1, 3) ) b. ( (2, 2) ) c. ( (3, 1) )

1. ( y = 3 )

a. ( (0, 3) ) b. ( (2, 3) ) c. ( (3, 3) )

1. ( 2(x - 1) + y = 6 )

a. ( (2, 4) ) b. ( (3, 2) ) c. ( (4, 0) )

1. ( 0.5y = x - 1 )

a. ( (2, 2) ) b. ( (3, 4) ) c. ( (4, 6) )

1. ( 3x - y = 5 )

a. ( (2, 1) ) b. ( (3, 4) ) c. ( (1, -2) )

1. ( y = -2x + 6 )

a. ( (1, 4) ) b. ( (2, 2) ) c. ( (3, 0) )

1. ( x + y = 4 )

a. ( (1, 3) ) b. ( (2, 2) ) c. ( (3, 2) )

Explanation:

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1) $y=2x$

Step1: Test pair A (1,2)

Substitute $x=1$, $y=2$: $2=2(1) \implies 2=2$ (True)

Step2: Test pair B (2,4)

Substitute $x=2$, $y=4$: $4=2(2) \implies 4=4$ (True)

Step3: Test pair C (3,5)

Substitute $x=3$, $y=5$: $5=2(3) \implies 5=6$ (False)

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2) $y=x+1$

Step1: Test pair A (0,1)

Substitute $x=0$, $y=1$: $1=0+1 \implies 1=1$ (True)

Step2: Test pair B (2,3)

Substitute $x=2$, $y=3$: $3=2+1 \implies 3=3$ (True)

Step3: Test pair C (3,5)

Substitute $x=3$, $y=5$: $5=3+1 \implies 5=4$ (False)

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3) $x+y=6$

Step1: Test pair A (2,4)

Substitute $x=2$, $y=4$: $2+4=6 \implies 6=6$ (True)

Step2: Test pair B (3,3)

Substitute $x=3$, $y=3$: $3+3=6 \implies 6=6$ (True)

Step3: Test pair C (1,5)

Substitute $x=1$, $y=5$: $1+5=6 \implies 6=6$ (True)

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4) $y=-x+4$

Step1: Test pair A (1,3)

Substitute $x=1$, $y=3$: $3=-1+4 \implies 3=3$ (True)

Step2: Test pair B (2,2)

Substitute $x=2$, $y=2$: $2=-2+4 \implies 2=2$ (True)

Step3: Test pair C (3,1)

Substitute $x=3$, $y=1$: $1=-3+4 \implies 1=1$ (True)

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5) $y=3$

Step1: Test pair A (0,3)

Substitute $y=3$: $3=3$ (True)

Step2: Test pair B (2,3)

Substitute $y=3$: $3=3$ (True)

Step3: Test pair C (3,3)

Substitute $y=3$: $3=3$ (True)

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6) $2(x-1)+y=6$

Step1: Test pair A (2,4)

Substitute $x=2$, $y=4$: $2(2-1)+4=2+4=6$ (True)

Step2: Test pair B (3,2)

Substitute $x=3$, $y=2$: $2(3-1)+2=4+2=6$ (True)

Step3: Test pair C (4,0)

Substitute $x=4$, $y=0$: $2(4-1)+0=6+0=6$ (True)

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7) $0.5y=x-1$

Step1: Test pair A (2,2)

Substitute $x=2$, $y=2$: $0.5(2)=2-1 \implies 1=1$ (True)

Step2: Test pair B (3,4)

Substitute $x=3$, $y=4$: $0.5(4)=3-1 \implies 2=2$ (True)

Step3: Test pair C (4,6)

Substitute $x=4$, $y=6$: $0.5(6)=4-1 \implies 3=3$ (True)

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8) $3x-y=5$

Step1: Test pair A (2,1)

Substitute $x=2$, $y=1$: $3(2)-1=6-1=5$ (True)

Step2: Test pair B (3,4)

Substitute $x=3$, $y=4$: $3(3)-4=9-4=5$ (True)

Step3: Test pair C (1,-2)

Substitute $x=1$, $y=-2$: $3(1)-(-2)=3+2=5$ (True)

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9) $y=-2x+6$

Step1: Test pair A (1,4)

Substitute $x=1$, $y=4$: $4=-2(1)+6 \implies 4=4$ (True)

Step2: Test pair B (2,2)

Substitute $x=2$, $y=2$: $2=-2(2)+6 \implies 2=2$ (True)

Step3: Test pair C (3,0)

Substitute $x=3$, $y=0$: $0=-2(3)+6 \implies 0=0$ (True)

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10) $x+y=4$

Step1: Test pair A (1,3)

Substitute $x=1$, $y=3$: $1+3=4$ (True)

Step2: Test pair B (2,2)

Substitute $x=2$, $y=2$: $2+2=4$ (True)

Step3: Test pair C (3,2)

Substitute $x=3$, $y=2$: $3+2=4 \implies 5=4$ (False)

Answer:

1. A. (1, 2), B. (2, 4)
2. A. (0, 1), B. (2, 3)
3. A. (2, 4), B. (3, 3), C. (1, 5)
4. A. (1, 3), B. (2, 2), C. (3, 1)
5. A. (0, 3), B. (2, 3), C. (3, 3)
6. A. (2, 4), B. (3, 2), C. (4, 0)
7. A. (2, 2), B. (3, 4), C. (4, 6)
8. A. (2, 1), B. (3, 4), C. (1, -2)
9. A. (1, 4), B. (2, 2), C. (3, 0)
10. A. (1, 3), B. (2, 2)