<span>Multiply the first equation by -2,and multiply the second equation by 1.</span><span><span>−2</span><span>(<span><span>x+<span>4y</span></span>=11</span>)</span></span><span>1<span>(<span><span><span>2x</span>+<span>2y</span></span>=<span>−8</span></span>)</span></span>Becomes:<span><span><span>−<span>2x</span></span>−<span>8y</span></span>=<span>−22</span></span><span><span><span>2x</span>+<span>2y</span></span>=<span>−8</span></span>Add these equations to eliminate x:<span><span>−<span>6y</span></span>=<span>−30</span></span>Then solve<span><span>−<span>6y</span></span>=<span>−30</span></span>for y:<span><span><span>−<span>6y</span></span><span>−6</span></span>=<span><span>−30</span><span>−6</span></span></span>(Divide both sides by -6)<span>y=5</span>Now that we've found y let's plug it back in to solve for x.Write down an original equation:<span><span>x+<span>4y</span></span>=11</span>Substitute5foryin<span><span><span>x+<span>4y</span></span>=11</span>:</span><span><span>x+<span><span>(4)</span><span>(5)</span></span></span>=11</span><span><span>x+20</span>=11</span>(Simplify both sides of the equation)<span><span><span>x+20</span>+<span>−20</span></span>=<span>11+<span>−20</span></span></span>(Add -20 to both sides)<span>x=<span>−9</span></span>Answer:<span><span>x=<span>−<span><span>9<span> and </span></span>y</span></span></span>=<span>5</span></span>
A
b
x−c=0
Step 1: Multiply both sides by b.
ax−bc=0
Step 2: Add bc to both sides.
ax−bc+bc=0+bc
ax=bc
Step 3: Divide both sides by x.
ax
x
=
bc
x
a=
bc
x
Answer:
a=
bc
x
The correct answer is option A. Erica is correct in saying that the two lines are not necessarily the same and we should also look at the y-intercepts before determining how many solutions there were. <span>Two lines with equal slopes could be the same line, but only if they have the same y-intercept.</span>
