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3 years ago

Y + 5x = 37 y = -x+13 Show your work Substitution one equation

Mathematics

1 answer:

lukranit [14]3 years ago

3 0

Answer:

x= 6

Step-by-step explanation:

In substitution, replace the y in the first equation with what y equals. In this case, y= -x+13.

-x+13 +5x= 37

4x+ 13= 37

4x= 24

x= 6

Explanation: First combination like terms, -x and 5. 5x-1x = 4x. Next, follow the opposite of PEMDAS. Adding and subtracting are last, so subtract the 13 on each side. All that's left is dividing the 4 on each side, and you're left with 6.

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Answer:

Below.

Step-by-step explanation:

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What are the y and x intercepts of y=3(x-6)²-9 and y=-2(x+5)²+3 .. Thanks

JulsSmile [24]

1.
$y=3(x-6)^2-9 \\ \\
\hbox{x-intercept - y=0} \\
0=3(x-6)^2-9 \\
9=3(x-6)^2 \ \ \ |\div 3 \\
3=(x-6)^2 \\
\sqrt{3}=\sqrt{(x-6)^2} \\
\pm \sqrt{3}=x-6 \\
\pm \sqrt{3}+6=x \\
x=6+\sqrt{3} \ \lor \ x=6-\sqrt{3}} \\ \\
\hbox{y-intercept - x=0} \\
y=3(0-6)^2-9 \\
y=3 \times (-6)^2-9 \\
y=3 \times 36-9 \\
y=108-9 \\
y=99 \\ \\
\boxed{\hbox{x-intercepts: } 6+\sqrt{3} \hbox{ and } 6-\sqrt{3}} \\
\boxed{\hbox{y-intercept: } 99}$

2.
$y=-2(x+5)^2+3 \\ \\
\hbox{x-intercept - y=0} \\
0=-2(x+5)^2+3 \\
-3=-2(x+5)^2 \ \ \ |\div (-2) \\
\frac{3}{2}=(x+5)^2 \\
\sqrt{\frac{3}{2}}=\sqrt{(x+5)^2} \\
\pm \sqrt{\frac{3}{2}}=x+5 \\
\pm \sqrt{\frac{3}{2}}-5=x \\
x=\sqrt{\frac{3}{2}}-5 \ \lor \ x=-\sqrt{\frac{3}{2}}-5 \\ \\
\hbox{y-intercept - x=0} \\
y=-2(0+5)^2+3 \\
y=-2 \times 5^2 +3 \\
y=-2 \times 25+3 \\
y=-50+3 \\
y=-47 \\ \\ \boxed{\hbox{x-intercepts: } \sqrt{\frac{3}{2}}-5 \hbox{ and } -\sqrt{\frac{3}{2}}-5} \\ \boxed{\hbox{y-intercept: } -47}$

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3 years ago

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