Answer:
Contains the point (-3, 5) and is PARALLEL to the line x − 5y = 6. Solve the equation for "y":: 5y = x- 6 y = (1/5)x-(6/5) The slope is 1/5 ---- Equation of line with slope = 1/5 passing thru point (-3,5) (y-5)/(x+3) = 1/ ...
<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>
The ratio of 1 to 3 is 1 : 3 or 1/3 (1 over 3)
