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Question Solve the linear equation 3x+7y=153x + 7y = 15 for either xx or yy.

Studdy Solution

STEP 1

Assumptions
1. We have a system of linear equations with two variables, x x and y y .
2. We are asked to isolate either x x or y y in the equation 3x+7y=15 3x + 7y = 15 .

STEP 2

We will choose to isolate y y for this example. To do this, we need to move all terms involving x x to the other side of the equation.
3x+7y=153x + 7y = 15

STEP 3

Subtract 3x 3x from both sides of the equation to move the term involving x x to the right side.
3x+7y−3x=15−3x3x + 7y - 3x = 15 - 3x

STEP 4

Simplify both sides of the equation.
7y=15−3x7y = 15 - 3x

STEP 5

Now, divide both sides of the equation by 7 7 to isolate y y .
7y7=15−3x7\frac{7y}{7} = \frac{15 - 3x}{7}

STEP 6

Simplify the equation to find the isolated y y .
y=157−3x7y = \frac{15}{7} - \frac{3x}{7}

STEP 7

We can leave the answer in this fractional form, or we can write it as a mixed number or decimal if needed. For now, we will leave it as fractions.
So, the isolated y y in terms of x x is:
y=157−3x7y = \frac{15}{7} - \frac{3x}{7}

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