8y+4z=7
6y+8z=41
To solve for y and z, we can use elimination method. We can multiply the first equation by 2 and subtract the second equation from it:
16y + 8z = 14
- (6y + 8z = 41)
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10y = -27
Dividing both sides by 10 gives:
y = -2.7
Substituting this value into the first equation gives:
8(-2.7) + 4z = 7
Simplifying and solving for z gives:
4z = 28.6
z = 7.15
Therefore, the solution is:
y = -2.7
z = 7.15
To solve the system of equations:
1. Multiply the first equation by 3 and the second equation by 4 to eliminate the y term:
24y + 12z = 21
24y + 32z = 164
2. Subtract the first equation from the second equation to eliminate the y term:
(24y + 32z) - (24y + 12z) = 164 - 21
20z = 143
3. Divide both sides of the equation by 20 to solve for z:
z = 143 / 20
z = 7.15
4. Substitute the value of z back into one of the original equations to solve for y. Let's use the first equation:
8y + 4(7.15) = 7
8y + 28.6 = 7
8y = 7 - 28.6
8y = -21.6
5. Divide both sides of the equation by 8 to solve for y:
y = -21.6 / 8
y = -2.7
Therefore, the solution to the system of equations is:
y = -2.7 and z = 7.15.