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3 years ago

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Use elimination to solve the system of equations:

1 answer:

tatyana61 [14]3 years ago

7 0

<span><span><span><span>2x</span>+<span>3y</span></span>=1</span>;<span><span>x+<span>4y</span></span>=<span>−2

</span></span></span>Steps:

<span>Multiply the second equation by -2, then add the equations together.

</span><span>(<span><span><span>2x</span>+<span>3y</span></span>=1</span>)

</span><span><span>−2</span><span>(<span><span>x+<span>4y</span></span>=<span>−2</span></span>)

</span></span>Becomes:

<span><span><span>2x</span>+<span>3y</span></span>=1

</span><span><span><span>−<span>2x</span></span>−<span>8y</span></span>=4

</span>Add these equations to eliminate x:

<span><span>−<span>5y</span></span>=5

</span>Then solve<span><span>−<span>5y</span></span>=5</span>for y:

<span><span><span>−<span>5y</span></span><span>−5</span></span>=<span>5<span>−5</span></span></span>(Divide both sides by -5)

<span>y=<span>−1

</span></span>Now that we've found y let's plug it back in to solve for x.

Write down an original equation:

<span><span><span>2x</span>+<span>3y</span></span>=1

</span>Substitute<span>−1</span>foryin<span><span><span><span>2x</span>+<span>3y</span></span>=1</span>:

</span><span><span><span>2x</span>+<span><span>(3)</span><span>(<span>−1</span>)</span></span></span>=1

</span><span><span><span>2x</span>−3</span>=1</span>(Simplify both sides of the equation)

<span><span><span><span>2x</span>−3</span>+3</span>=<span>1+3</span></span>(Add 3 to both sides)

<span><span>2x</span>=4

</span><span><span><span>2x</span>2</span>=<span>42</span></span>(Divide both sides by 2)

<span>x=2

</span>Answer:

<span><span>x=<span><span>2<span> and </span></span>y</span></span>=<span>−<span>1

</span></span></span>

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