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What is the solution of the system of equations?

Mathematics
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3u + v = 7 3u = v + 23 **** See **** below for graphical solution **** Rearrange the second equation: 3u - v = 23 3u + v = 7 6u = 30 (add the two equations) u = 5 v = 7 - 3(5) = -8 solution is u = 5, v = -8 (the point (5,-8) on the u-v plane) since there is one solution, the two lines intersect in one point, and the system is consistent and independent ******* Graphical solution approach ******* To graph the lines (in the u-v plane--u= horizontal axis): 3u + v = 7 (0,7) is v-intercept (7/3,0) is the u-intercept) 3u = v + 23 (0,-23) is the v-intercept (23/3,0) is the u-intercept connect the two intercepts for each line, and find the point of intersection or, converting to v = mu + b form: v = -3u + 7 (slope -3, v-intercept 7) v = 3u - 23 (slope 3, v-intercept -23) draw lines this way and find intersection which will be (5,-8)
Here is the equations, 2x+2y-3z = -6 3x + 5y +4z= -3 2x + 3y +4z = -1o
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Simplifying 2x + 2y + -3z = -6 Solving 2x + 2y + -3z = -6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2y' to each side of the equation. 2x + 2y + -2y + -3z = -6 + -2y Combine like terms: 2y + -2y = 0 2x + 0 + -3z = -6 + -2y 2x + -3z = -6 + -2y Add '3z' to each side of the equation. 2x + -3z + 3z = -6 + -2y + 3z Combine like terms: -3z + 3z = 0 2x + 0 = -6 + -2y + 3z 2x = -6 + -2y + 3z Divide each side by '2'. x = -3 + -1y + 1.5z Simplifying x = -3 + -1y + 1.5z
Simplifying 3x + 5y + 4z = -3 Solving 3x + 5y + 4z = -3 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5y' to each side of the equation. 3x + 5y + -5y + 4z = -3 + -5y Combine like terms: 5y + -5y = 0 3x + 0 + 4z = -3 + -5y 3x + 4z = -3 + -5y Add '-4z' to each side of the equation. 3x + 4z + -4z = -3 + -5y + -4z Combine like terms: 4z + -4z = 0 3x + 0 = -3 + -5y + -4z 3x = -3 + -5y + -4z Divide each side by '3'. x = -1 + -1.666666667y + -1.333333333z Simplifying x = -1 + -1.666666667y + -1.333333333z
Simplifying 2x + 3y + 4z = -1o Solving 2x + 3y + 4z = -1o Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3y' to each side of the equation. 2x + 3y + -3y + 4z = -1o + -3y Combine like terms: 3y + -3y = 0 2x + 0 + 4z = -1o + -3y 2x + 4z = -1o + -3y Add '-4z' to each side of the equation. 2x + 4z + -4z = -1o + -3y + -4z Combine like terms: 4z + -4z = 0 2x + 0 = -1o + -3y + -4z 2x = -1o + -3y + -4z Divide each side by '2'. x = -0.5o + -1.5y + -2z Simplifying x = -0.5o + -1.5y + -2z
Do you need anymore help on equations? :)
Nope thank you soo much!

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