Graph the system of equations. {8x+8y=642x−2y=−4
1 answer:
<span>The graph is attached.
Explanation:
We can use the x- and y-intercepts to graph. The x-intercept of the first equation is 8, and the y-intercept is 8. The x-intercept of the second equation is -2, and the y-intercept is 2.
<span>
x-intercepts are where the data crosses the x-axis. At every one of these points, the y-coordinate will be 0; therefore we can substitute 0 for y and solve to get the value of the x-intercept.
For the first equation, we would have
8x+8(0)=64
8x=64.
Divide both sides by 8:
8x/8 = 64/8
x=8.
For the second equation,
2x-2(0)=-4
2x=-4.
Divide both sides by 2:
2x/2 = -4/2
x=-2.
y-intercepts are where the data crosses the y-axis. At every one of these points, the x-coordinate will be 0; therefore we can substitute 0 for x and solve to get the value of the y-intercept.
For the first equation,
8(0)+8y=64
8y=64.
Divide both sides by 8:
8y/8 = 64/8
y=8.
For the second equation,
2(0)-2y=-4
-2y=-4.
Divide both sides by -2:
-2y/-2 = -4/-2
y=2.
Plot these points for both equations and connect them to draw the line.</span></span>
Explanation:
We can use the x- and y-intercepts to graph. The x-intercept of the first equation is 8, and the y-intercept is 8. The x-intercept of the second equation is -2, and the y-intercept is 2.
<span>
x-intercepts are where the data crosses the x-axis. At every one of these points, the y-coordinate will be 0; therefore we can substitute 0 for y and solve to get the value of the x-intercept.
For the first equation, we would have
8x+8(0)=64
8x=64.
Divide both sides by 8:
8x/8 = 64/8
x=8.
For the second equation,
2x-2(0)=-4
2x=-4.
Divide both sides by 2:
2x/2 = -4/2
x=-2.
y-intercepts are where the data crosses the y-axis. At every one of these points, the x-coordinate will be 0; therefore we can substitute 0 for x and solve to get the value of the y-intercept.
For the first equation,
8(0)+8y=64
8y=64.
Divide both sides by 8:
8y/8 = 64/8
y=8.
For the second equation,
2(0)-2y=-4
-2y=-4.
Divide both sides by -2:
-2y/-2 = -4/-2
y=2.
Plot these points for both equations and connect them to draw the line.</span></span>
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Hello!
This is a question about ratios and relating them to multiples of the ratio.
We are given that a recipe for cooking rice requires 14 cups of boiling water for every 8 cups of rice.
Then we are asked how many cups of rice are needing to be added if we have 28 cups of boiling water.
Since 28 is two times 14, and assuming that this ratio is proportional, we can multiply the cups of rice by 2 to find the equal ratio.
That means that 16 cups of rice should be added if we have 28 cups of boiling water.
In terms of ratios, we can set up the following proportion.
Then here, we can cross multiply and solve for .
Hope this helps!