Let's use substitution:
-2x + 5y = 20−2x+5y=20
x + 4y = 16x+4y=16
We need to solve for xx in the second equation
x = 16 - 4yx=16−4y
Now we substitute (16 - 4y)(16−4y) for xx in the first equation
-2(16 - 4y) + 5y = 20−2(16−4y)+5y=20
distribute the -2−2
-32 + 8y + 5y = 20−32+8y+5y=20
Solve for yy. Add 3232 to both sides
13y = 5213y=52
Divide by 1313 on both sides
y = 4y=4
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
We have yy, let's find xx:
x = 16 - 4yx=16−4y
x = 16 - 4(4)x=16−4(4)
x = 16 - 16x=16−16
x = 0x=0
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To check our work, let's plug our values for xx and yy into the first equation and see if it equals 2020:
-2(0) + 5(4)−2(0)+5(4)
0 + 200+20
2020 EQUALS 2020! We were right
