Answered

If the ordered pairs [tex]\((a, -1)\)[/tex] and [tex]\((5, b)\)[/tex] belong to [tex]\(\{(x, y): y = 2x - 3\}\)[/tex], find the values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex].



Answer :

GinnyAnswer
To find the values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex], we start by using the given equation of the line:

[tex]\[ y = 2x - 3 \][/tex]

### Step 1: Finding [tex]\(a\)[/tex]

We know the ordered pair [tex]\((a, -1)\)[/tex] belongs to the line. Hence, substituting [tex]\(y = -1\)[/tex] and [tex]\(x = a\)[/tex] into the equation:

[tex]\[ -1 = 2a - 3 \][/tex]

To solve for [tex]\(a\)[/tex], we first add 3 to both sides of the equation:

[tex]\[ -1 + 3 = 2a \][/tex]

Which simplifies to:

[tex]\[ 2 = 2a \][/tex]

Next, we divide both sides by 2:

[tex]\[ a = 1 \][/tex]

Thus, the value of [tex]\(a\)[/tex] is:

[tex]\[ a = 1 \][/tex]

### Step 2: Finding [tex]\(b\)[/tex]

We know the ordered pair [tex]\((5, b)\)[/tex] belongs to the line. Hence, substituting [tex]\(x = 5\)[/tex] into the equation and solving for [tex]\(y = b\)[/tex]:

[tex]\[ b = 2(5) - 3 \][/tex]

This simplifies to:

[tex]\[ b = 10 - 3 \][/tex]

Which further simplifies to:

[tex]\[ b = 7 \][/tex]

Thus, the value of [tex]\(b\)[/tex] is:

[tex]\[ b = 7 \][/tex]

### Summary

The values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex] are:

[tex]\[ a = 1 \quad \text{and} \quad b = 7 \][/tex]

Other Questions