Answer:
(2,2)
Step-by-step explanation:
Since the y's already have different signs, you can multiply the top equation by 2 and eliminate the y's. You may instead multiply the bottom equation by -3 and eliminate the x's. Either way, solve for the variable that is left. Plug that answer back into either equation and solve for the other variable. The answer is (2,2).
<em>3x−y=4;x+2y=6</em>
<em>Step: Solve3x−y=4for y:</em>
<em>3x−y+−3x=4+−3x(Add -3x to both sides)</em>
<em>−y=−3x+4</em>
<em>−y</em>
<em>−1</em>
<em>=</em>
<em>−3x+4</em>
<em>−1</em>
<em>(Divide both sides by -1)</em>
<em>y=3x−4</em>
<em>Step: Substitute3x−4foryinx+2y=6:</em>
<em>x+2y=6</em>
<em>x+2(3x−4)=6</em>
<em>7x−8=6(Simplify both sides of the equation)</em>
<em>7x−8+8=6+8(Add 8 to both sides)</em>
<em>7x=14</em>
<em>7x</em>
<em>7</em>
<em>=</em>
<em>14</em>
<em>7</em>
<em>(Divide both sides by 7)</em>
<em>x=2</em>
<em>Step: Substitute2forxiny=3x−4:</em>
<em>y=3x−4</em>
<em>y=(3)(2)−4</em>
<em>y=2(Simplify both sides of the equation)</em>
<em>Answer:</em>
<em>x=2 and y=2</em>
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