Answer:
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Step-by-step explanation:
Hi -
What you want to do here is solve the equation by substitution.
To do that, you solve one of the equations for y. then plug that into the other equation so you have an equation with only x as the variable.
1) Solve either equation for y. Lets go with the first one:
4x+5y=102
Subtract 4x from each side:
5y=102-4x
Divide both sides by 5
y=(102-4x)/5
2) Plug this value for y into the other equation we started with:
7x+5y = 126
7x + 5((102-4x)/5) = 126
3) Solve the resulting equation for x.
Since we are multiplying and dividing (102-4x) by 5 the 2 5s cancel each other out
7x + 5((102-4x)/5) = 126
7x + 102 - 4x = 126
Combine the 2 x terms:
3x+102=126
subtract 102 from each side:
3x = 24
Divide both sides by 3:
x=8
Once we have a value for x, we can plug that number into either one of our starting equations to solve for y.
4x + 5y = 102; if x = 8
32+5y = 102
subtract 32 from each side:
5y = 70
Divide both sides by 5:
y = 14
So x = 8 and y = 14.
You can check your work by plugging these numbers both into your 2 initial equations.
4x+5y=102; 4*8+5*14 = 102
7x+5y=126; 7*8 +5*14 = 126
