Rewrite the following equation in standard form.y=2x+3Hint: The standard form of a linear equation is Ax+By=C where A and B are not both zero, and A, B, and C are integers whose GCF is 1.
Q. Rewrite the following equation in standard form.y=2x+3Hint: The standard form of a linear equation is Ax+By=C where A and B are not both zero, and A, B, and C are integers whose GCF is 1.
Rearrange terms for standard form: To convert the equation y=2x+3 into standard form, we need to rearrange the terms so that the x and y terms are on one side of the equation and the constant is on the other side. We want it in the form Ax+By=C.
Subtract 2x: Subtract 2x from both sides of the equation to move the x term to the left side of the equation. This gives us:y−2x=3−2x
Simplify the equation: Simplify the equation by combining like terms. Since there are no like terms on the right side, we just rewrite the equation as: −2x+y=3
Make A positive: The standard form of a linear equation is Ax+By=C, where A is a positive integer. Since −2 is negative, we multiply the entire equation by −1 to make A positive:−1(−2x+y)=−1(3)
Distribute −1: Distribute the −1 across each term in the equation: 2x−y=−3
Final standard form: The equation 2x−y=−3 is now in standard form, with A=2, B=−1, and C=−3. The greatest common factor (GCF) of A, B, and C is 1, which satisfies the conditions for standard form.
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